Mckvie - 23-24 April 2018- Pre-training Assessment - 2

1. Find the highest common factor of 36 and 84.

4

6

12

18

The highest common factor (HCF) of two numbers is the largest number that divides both numbers without leaving a remainder. To find the HCF of 36 and 84, we can list the factors of each number and find the largest number that appears in both lists. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. The largest number that appears in both lists is 12, so the HCF of 36 and 84 is 12.

Explanation

The highest common factor (HCF) of two numbers is the largest number that divides both numbers without leaving a remainder. To find the HCF of 36 and 84, we can list the factors of each number and find the largest number that appears in both lists. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. The largest number that appears in both lists is 12, so the HCF of 36 and 84 is 12.

2. A memory chip has 8 data lines and 9 address lines. How many bytes can be stored on it?

511

512

500

516

A memory chip with 8 data lines and 9 address lines can store 2^9 bytes of data. This is because the number of address lines determines the number of unique addresses that can be accessed, and each address can store 1 byte of data. Therefore, 2^9 equals 512, so 512 bytes can be stored on the memory chip.

Explanation

A memory chip with 8 data lines and 9 address lines can store 2^9 bytes of data. This is because the number of address lines determines the number of unique addresses that can be accessed, and each address can store 1 byte of data. Therefore, 2^9 equals 512, so 512 bytes can be stored on the memory chip.

3. The fourth proportional to 5, 8, 15 is:

18

24

19

20

The fourth proportional to 5, 8, and 15 can be found by multiplying the third term by the ratio of the second and first terms. In this case, the third term is 15, the second term is 8, and the first term is 5. So, the ratio of the second and first terms is 8/5. Multiplying this ratio by the third term gives us 15 * (8/5) = 24. Therefore, the fourth proportional to 5, 8, and 15 is 24.

Explanation

The fourth proportional to 5, 8, and 15 can be found by multiplying the third term by the ratio of the second and first terms. In this case, the third term is 15, the second term is 8, and the first term is 5. So, the ratio of the second and first terms is 8/5. Multiplying this ratio by the third term gives us 15 * (8/5) = 24. Therefore, the fourth proportional to 5, 8, and 15 is 24.

4. Predict the output of the following code main() { char s[ ]="man"; int i; for(i=0;s[ i ];i++) printf("\n%c%c%c%c",s[ i ],*(s+i),*(i+s),i[s]); }

Mmm

Mmmmm

Mmmmmm

The given code snippet is a C program that prints a specific pattern using the characters in the string "man".

The for loop iterates over each character in the string "man" using the variable "i".

Inside the loop, the printf statement prints the characters in different ways:
- "%c" prints the character at index "i" in the string "s"
- "*(s+i)" also prints the character at index "i" in the string "s"
- "*(i+s)" and "i[s]" are equivalent to "*(s+i)" and also print the character at index "i" in the string "s"

The pattern printed by the printf statement is "%c%c%c%c", where "%c" represents the characters from the string "man".

Therefore, the output of the code will be "mmmm aaaa nnnn".

Explanation

The given code snippet is a C program that prints a specific pattern using the characters in the string "man".

The for loop iterates over each character in the string "man" using the variable "i".

Inside the loop, the printf statement prints the characters in different ways:
- "%c" prints the character at index "i" in the string "s"
- "*(s+i)" also prints the character at index "i" in the string "s"
- "*(i+s)" and "i[s]" are equivalent to "*(s+i)" and also print the character at index "i" in the string "s"

The pattern printed by the printf statement is "%c%c%c%c", where "%c" represents the characters from the string "man".

Therefore, the output of the code will be "mmmm aaaa nnnn".

5. If 0.75 : x :: 5 : 8, then x is equal to:

1.12

1.2

1.25

1.3

The given ratio can be written as 0.75/x = 5/8. Cross-multiplying, we get 0.75 * 8 = 5 * x. Simplifying further, we find that 6 = 5x. Dividing both sides by 5, we find that x = 1.2.

Explanation

The given ratio can be written as 0.75/x = 5/8. Cross-multiplying, we get 0.75 * 8 = 5 * x. Simplifying further, we find that 6 = 5x. Dividing both sides by 5, we find that x = 1.2.

6. From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 100 m high, the distance of point P from the foot of the tower is:

149 m

156 m

173 m

200 m

The angle of elevation of 30º indicates that we have a right triangle. The height of the tower is the opposite side and the distance from point P to the foot of the tower is the adjacent side. The tangent of the angle is equal to the opposite side divided by the adjacent side. Therefore, we can use the tangent of 30º to find the ratio between the height of the tower and the distance from point P. By rearranging the formula, we can solve for the distance from point P, which is approximately 173 m.

Explanation

The angle of elevation of 30º indicates that we have a right triangle. The height of the tower is the opposite side and the distance from point P to the foot of the tower is the adjacent side. The tangent of the angle is equal to the opposite side divided by the adjacent side. Therefore, we can use the tangent of 30º to find the ratio between the height of the tower and the distance from point P. By rearranging the formula, we can solve for the distance from point P, which is approximately 173 m.

7. The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:

101

107

111

185

The product of two numbers is 4107 and their highest common factor (H.C.F.) is 37. To find the greater number, we need to divide the product by the H.C.F. The result is 4107/37 = 111. Therefore, the greater number is 111.

Explanation

The product of two numbers is 4107 and their highest common factor (H.C.F.) is 37. To find the greater number, we need to divide the product by the H.C.F. The result is 4107/37 = 111. Therefore, the greater number is 111.

8. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

120 METRES

180 METRES

324 METRES

150 METRES

The length of the train can be calculated using the formula: Distance = Speed x Time. In this case, the speed is given as 60 km/hr, which needs to be converted to m/s by multiplying it by 5/18. The time taken to cross the pole is given as 9 seconds. Plugging these values into the formula, we get Distance = (60 x 5/18) x 9 = 150 meters. Therefore, the length of the train is 150 meters.

Explanation

The length of the train can be calculated using the formula: Distance = Speed x Time. In this case, the speed is given as 60 km/hr, which needs to be converted to m/s by multiplying it by 5/18. The time taken to cross the pole is given as 9 seconds. Plugging these values into the formula, we get Distance = (60 x 5/18) x 9 = 150 meters. Therefore, the length of the train is 150 meters.

9. In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?

20

30

40

50

If there is a meal for 120 men or 200 children, it means that the ratio of men to children is 120:200 or 3:5. If 150 children have already taken the meal, there are 50 children left. To find out how many men can be catered to with the remaining meal, we need to find a ratio equivalent to 50 children. By simplifying the ratio 3:5, we find that for every 1 child, there are 3/5 men. Therefore, for 50 children, there will be (3/5) * 50 = 30 men catered to with the remaining meal.

Explanation

If there is a meal for 120 men or 200 children, it means that the ratio of men to children is 120:200 or 3:5. If 150 children have already taken the meal, there are 50 children left. To find out how many men can be catered to with the remaining meal, we need to find a ratio equivalent to 50 children. By simplifying the ratio 3:5, we find that for every 1 child, there are 3/5 men. Therefore, for 50 children, there will be (3/5) * 50 = 30 men catered to with the remaining meal.

10. Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? A. 2 years B. 4 years C. 6 years D. 8 years

2 Years

4 Years

6 Years

8 Years

Since Ayesha's brother is four years younger than her, we can assume that the age difference between Ayesha's father and mother is also four years. If Ayesha's father was 38 when she was born, then her mother would have been 34 at that time. Similarly, if her mother was 36 when her brother was born, then her father would have been 40 at that time. Therefore, the difference between the ages of her parents is 40 - 34 = 6 years.

Explanation

Since Ayesha's brother is four years younger than her, we can assume that the age difference between Ayesha's father and mother is also four years. If Ayesha's father was 38 when she was born, then her mother would have been 34 at that time. Similarly, if her mother was 36 when her brother was born, then her father would have been 40 at that time. Therefore, the difference between the ages of her parents is 40 - 34 = 6 years.

11. An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?

144 Degrees

150 Degrees

168 Degres

180 Degrees

The hour hand of a clock completes a full rotation of 360 degrees in 12 hours. From 8 o'clock in the morning to 2 o'clock in the afternoon, there are 6 hours. Therefore, the hour hand will rotate 6/12 or 1/2 of a full rotation, which is equal to 180 degrees.

Explanation

The hour hand of a clock completes a full rotation of 360 degrees in 12 hours. From 8 o'clock in the morning to 2 o'clock in the afternoon, there are 6 hours. Therefore, the hour hand will rotate 6/12 or 1/2 of a full rotation, which is equal to 180 degrees.

12. The output of code below is #include void main() { int x=0; if(x==0) printf("hi"); else printf("how are u"); printf("hello"); }

Hi

How are you

Hello

Hihello

The code starts by initializing the variable x to 0. It then enters the if statement and checks if x is equal to 0. Since x is indeed equal to 0, the code executes the printf statement "hi". After that, it reaches the printf statement "hello" outside of the if statement. Therefore, the output of the code is "hihello".

Explanation

The code starts by initializing the variable x to 0. It then enters the if statement and checks if x is equal to 0. Since x is indeed equal to 0, the code executes the printf statement "hi". After that, it reaches the printf statement "hello" outside of the if statement. Therefore, the output of the code is "hihello".

13. Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 % .p.a. How much amount will Albert get on maturity of the fixed deposit?

Rs 8600

Rs 8620

Rs 8820

None of These

Albert invested Rs. 8000 in a fixed deposit scheme for 2 years at a compound interest rate of 5% per annum. Compound interest is calculated by the formula A = P(1 + r/n)^(nt), where A is the amount on maturity, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time period in years. In this case, the interest is compounded annually (n=1). Plugging in the values, A = 8000(1 + 0.05/1)^(1*2) = Rs. 8820. Therefore, Albert will get Rs. 8820 on maturity of the fixed deposit.

Explanation

Albert invested Rs. 8000 in a fixed deposit scheme for 2 years at a compound interest rate of 5% per annum. Compound interest is calculated by the formula A = P(1 + r/n)^(nt), where A is the amount on maturity, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time period in years. In this case, the interest is compounded annually (n=1). Plugging in the values, A = 8000(1 + 0.05/1)^(1*2) = Rs. 8820. Therefore, Albert will get Rs. 8820 on maturity of the fixed deposit.

14. The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:

20

23

169

None of These

Let's assume the two numbers as x and y. We are given that the product of these two numbers is 120, so we can write the equation xy = 120. Additionally, the sum of their squares is given as 289, so we can write the equation x^2 + y^2 = 289. By solving these two equations simultaneously, we find that x = 15 and y = 8. Therefore, the sum of the numbers is 15 + 8 = 23.

Explanation

Let's assume the two numbers as x and y. We are given that the product of these two numbers is 120, so we can write the equation xy = 120. Additionally, the sum of their squares is given as 289, so we can write the equation x^2 + y^2 = 289. By solving these two equations simultaneously, we find that x = 15 and y = 8. Therefore, the sum of the numbers is 15 + 8 = 23.

15. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

120 M

240 M

300 M

None of These

The train takes 36 seconds to pass the platform and 20 seconds to pass the man. This means that the train spends an extra 16 seconds to pass the entire length of the platform, which is equal to the time it takes to cover the length of the platform. Since the speed of the train is given as 54 km/hr, we can convert it to meters per second by multiplying by 5/18. Therefore, the length of the platform can be calculated by multiplying the speed of the train (in m/s) by the extra time it takes to pass the platform. This gives us 54 * (5/18) * 16 = 240 meters. Therefore, the correct answer is 240 M.

Explanation

The train takes 36 seconds to pass the platform and 20 seconds to pass the man. This means that the train spends an extra 16 seconds to pass the entire length of the platform, which is equal to the time it takes to cover the length of the platform. Since the speed of the train is given as 54 km/hr, we can convert it to meters per second by multiplying by 5/18. Therefore, the length of the platform can be calculated by multiplying the speed of the train (in m/s) by the extra time it takes to pass the platform. This gives us 54 * (5/18) * 16 = 240 meters. Therefore, the correct answer is 240 M.

16. Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?

Rs 200

RS 250

Rs 300

None of These

Let's assume that Y is paid Rs. x per week. According to the given information, X is paid 120% of what Y is paid. So, X is paid 1.2x per week. The total amount paid to both X and Y is Rs. 550. Therefore, we can write the equation: x + 1.2x = 550. Simplifying this equation, we get 2.2x = 550. Dividing both sides by 2.2, we find that x = 250. Therefore, Y is paid Rs. 250 per week.

Explanation

Let's assume that Y is paid Rs. x per week. According to the given information, X is paid 120% of what Y is paid. So, X is paid 1.2x per week. The total amount paid to both X and Y is Rs. 550. Therefore, we can write the equation: x + 1.2x = 550. Simplifying this equation, we get 2.2x = 550. Dividing both sides by 2.2, we find that x = 250. Therefore, Y is paid Rs. 250 per week.

17. A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

2 : 1

3 : 2

25 : 18

27 : 23

When three smaller cubes with side lengths of 3 cm, 4 cm, and 5 cm are melted to form a larger cube, the side length of the larger cube can be found by taking the cube root of the sum of the volumes of the smaller cubes. The volume of a cube is equal to the side length cubed. So, the volume of the larger cube is (3^3 + 4^3 + 5^3) = 216 cm^3. Taking the cube root of 216 gives us a side length of 6 cm for the larger cube.

The total surface area of a cube is equal to 6 times the side length squared. So, the total surface area of the smaller cubes is (6 x 3^2) + (6 x 4^2) + (6 x 5^2) = 342 cm^2. The total surface area of the larger cube is 6 x 6^2 = 216 cm^2.

The ratio of the total surface areas of the smaller cubes to the larger cube is therefore 342 : 216, which simplifies to 25 : 18.

Explanation

When three smaller cubes with side lengths of 3 cm, 4 cm, and 5 cm are melted to form a larger cube, the side length of the larger cube can be found by taking the cube root of the sum of the volumes of the smaller cubes. The volume of a cube is equal to the side length cubed. So, the volume of the larger cube is (3^3 + 4^3 + 5^3) = 216 cm^3. Taking the cube root of 216 gives us a side length of 6 cm for the larger cube.

The total surface area of a cube is equal to 6 times the side length squared. So, the total surface area of the smaller cubes is (6 x 3^2) + (6 x 4^2) + (6 x 5^2) = 342 cm^2. The total surface area of the larger cube is 6 x 6^2 = 216 cm^2.

The ratio of the total surface areas of the smaller cubes to the larger cube is therefore 342 : 216, which simplifies to 25 : 18.

18. All the trees in the park are flowering trees. Some of the trees in the park are dogwoods. All dogwoods in the park are flowering trees. If the first two statements are true, the third statement is

1

UNCERTAIN

The third statement is true. This can be deduced from the first two statements. Since all the trees in the park are flowering trees and some of the trees in the park are dogwoods, it implies that the dogwoods in the park are also flowering trees. Therefore, the third statement is true.

Explanation

The third statement is true. This can be deduced from the first two statements. Since all the trees in the park are flowering trees and some of the trees in the park are dogwoods, it implies that the dogwoods in the park are also flowering trees. Therefore, the third statement is true.

19. 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

10

13

14

15

If 39 persons can repair a road in 12 days, working 5 hours a day, it means that the total work required to repair the road is equal to 39 x 12 x 5 = 2340 person-hours.

To find out how many days will 30 persons, working 6 hours a day, complete the work, we need to calculate the total person-hours they can work.

30 persons working 6 hours a day can work a total of 30 x 6 = 180 person-hours per day.

Therefore, the number of days required to complete the work is 2340 / 180 = 13 days.

Explanation

If 39 persons can repair a road in 12 days, working 5 hours a day, it means that the total work required to repair the road is equal to 39 x 12 x 5 = 2340 person-hours.

To find out how many days will 30 persons, working 6 hours a day, complete the work, we need to calculate the total person-hours they can work.

30 persons working 6 hours a day can work a total of 30 x 6 = 180 person-hours per day.

Therefore, the number of days required to complete the work is 2340 / 180 = 13 days.

20. Predict the output of the following code : main() { int x=5,*p=&x; printf("%d",++(*p)); }

4

5

6

7

The code declares a variable x with a value of 5 and a pointer p that points to the memory address of x. The printf statement increments the value stored at the memory address pointed to by p by 1 and then prints the value. Since the value of x is 5 initially, incrementing it by 1 results in 6. Therefore, the output of the code is 6.

Explanation

The code declares a variable x with a value of 5 and a pointer p that points to the memory address of x. The printf statement increments the value stored at the memory address pointed to by p by 1 and then prints the value. Since the value of x is 5 initially, incrementing it by 1 results in 6. Therefore, the output of the code is 6.

21. The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:

12 Years

14 Years

18 Years

20 Years

Six years ago, the father's age was five times the age of the son. This means that if we subtract 6 from the present age of the father and the son, the father's age would still be five times the son's age. Let's assume the present age of the son is x. So, the present age of the father would be 60 - x. Six years ago, the father's age would be 60 - x - 6, and the son's age would be x - 6. According to the given information, 60 - x - 6 = 5(x - 6). Solving this equation, we get x = 14. After 6 years, the son's age will be 14 + 6 = 20 years.

Explanation

Six years ago, the father's age was five times the age of the son. This means that if we subtract 6 from the present age of the father and the son, the father's age would still be five times the son's age. Let's assume the present age of the son is x. So, the present age of the father would be 60 - x. Six years ago, the father's age would be 60 - x - 6, and the son's age would be x - 6. According to the given information, 60 - x - 6 = 5(x - 6). Solving this equation, we get x = 14. After 6 years, the son's age will be 14 + 6 = 20 years.

22. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

36

45

48

49

The time taken by the slower train to cross the faster train can be calculated by adding the lengths of both trains and dividing it by the relative speed between the two trains. In this case, the total length of both trains is 2 km (1.10 km + 0.9 km) and the relative speed is 150 km/hr (60 km/hr + 90 km/hr). Converting the relative speed to meters per second, we get 41.67 m/s (150 km/hr * 1000 m/3600 s). Dividing the total length by the relative speed, we get 48 seconds.

Explanation

The time taken by the slower train to cross the faster train can be calculated by adding the lengths of both trains and dividing it by the relative speed between the two trains. In this case, the total length of both trains is 2 km (1.10 km + 0.9 km) and the relative speed is 150 km/hr (60 km/hr + 90 km/hr). Converting the relative speed to meters per second, we get 41.67 m/s (150 km/hr * 1000 m/3600 s). Dividing the total length by the relative speed, we get 48 seconds.

23. A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?

10

20

21

25

Let's assume that the initial amount of liquid A in the can is 7x and the initial amount of liquid B is 5x. When 9 liters of the mixture are drawn off, the amount of liquid A remaining is (7x - (7/12) * 9) and the amount of liquid B remaining is (5x - (5/12) * 9). After filling the can with liquid B, the amount of liquid A becomes (7x - (7/12) * 9) and the amount of liquid B becomes (5x - (5/12) * 9 + 9). We are given that the ratio of A to B becomes 7:9, so we can set up the equation (7x - (7/12) * 9) / (5x - (5/12) * 9 + 9) = 7/9. Solving this equation, we find that x = 3. Therefore, the initial amount of liquid A in the can was 7x = 7 * 3 = 21 liters.

Explanation

Let's assume that the initial amount of liquid A in the can is 7x and the initial amount of liquid B is 5x. When 9 liters of the mixture are drawn off, the amount of liquid A remaining is (7x - (7/12) * 9) and the amount of liquid B remaining is (5x - (5/12) * 9). After filling the can with liquid B, the amount of liquid A becomes (7x - (7/12) * 9) and the amount of liquid B becomes (5x - (5/12) * 9 + 9). We are given that the ratio of A to B becomes 7:9, so we can set up the equation (7x - (7/12) * 9) / (5x - (5/12) * 9 + 9) = 7/9. Solving this equation, we find that x = 3. Therefore, the initial amount of liquid A in the can was 7x = 7 * 3 = 21 liters.

24. Which of the following does POP stand for?

Post Office Protocol

Peer over peer

Private Office Protocol

Post Optical Protocol

POP stands for Post Office Protocol. It is an internet standard protocol used by email clients to retrieve email from a mail server. It allows the user to download messages from the server onto their local device, after which the messages are typically deleted from the server. This protocol is commonly used for accessing email in a client-server relationship, where the email client connects to the mail server to retrieve messages.

Explanation

POP stands for Post Office Protocol. It is an internet standard protocol used by email clients to retrieve email from a mail server. It allows the user to download messages from the server onto their local device, after which the messages are typically deleted from the server. This protocol is commonly used for accessing email in a client-server relationship, where the email client connects to the mail server to retrieve messages.

25. The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:

28

32

40

64

Let the numbers be 2x and 3x. The LCM of 2x and 3x is 6x. Given that the LCM is 48, we can find x by dividing 48 by 6, which gives x = 8. Therefore, the numbers are 2x = 2(8) = 16 and 3x = 3(8) = 24. The sum of the numbers is 16 + 24 = 40.

Explanation

Let the numbers be 2x and 3x. The LCM of 2x and 3x is 6x. Given that the LCM is 48, we can find x by dividing 48 by 6, which gives x = 8. Therefore, the numbers are 2x = 2(8) = 16 and 3x = 3(8) = 24. The sum of the numbers is 16 + 24 = 40.

26. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

9:00 AM

10:00 AM

10.30 AM

11:00 AM

The first train starts at 7 a.m. and travels for 3 hours at a speed of 20 kmph, covering a distance of 60 km. The second train starts at 8 a.m. and travels for 2 hours at a speed of 25 kmph, covering a distance of 50 km. The total distance covered by both trains is 110 km, which is the distance between the two stations. Therefore, they will meet after 3 hours, which is at 10:00 AM.

Explanation

The first train starts at 7 a.m. and travels for 3 hours at a speed of 20 kmph, covering a distance of 60 km. The second train starts at 8 a.m. and travels for 2 hours at a speed of 25 kmph, covering a distance of 50 km. The total distance covered by both trains is 110 km, which is the distance between the two stations. Therefore, they will meet after 3 hours, which is at 10:00 AM.

27. The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?

4

8

16

None of These

Let's assume the two-digit number is 10x + y, where x and y are the digits. According to the given information, the number obtained by interchanging the digits is 10y + x. The difference between these two numbers is (10x + y) - (10y + x) = 9x - 9y = 36. Simplifying this equation, we get x - y = 4.

The sum of the digits is x + y, and the difference of the digits is x - y. The ratio between the digits is given as 1:2, which means x = 2y. Substituting this value in the equation x - y = 4, we get 2y - y = 4, which simplifies to y = 4.

Therefore, the difference between the sum and the difference of the digits is (x + y) - (x - y) = 2y = 2(4) = 8.

Explanation

Let's assume the two-digit number is 10x + y, where x and y are the digits. According to the given information, the number obtained by interchanging the digits is 10y + x. The difference between these two numbers is (10x + y) - (10y + x) = 9x - 9y = 36. Simplifying this equation, we get x - y = 4.

The sum of the digits is x + y, and the difference of the digits is x - y. The ratio between the digits is given as 1:2, which means x = 2y. Substituting this value in the equation x - y = 4, we get 2y - y = 4, which simplifies to y = 4.

Therefore, the difference between the sum and the difference of the digits is (x + y) - (x - y) = 2y = 2(4) = 8.

28. Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?

3.5

4.5

5.6

6.5

Sam purchased 20 dozens of toys, which is equal to 240 toys. He bought each dozen at a rate of Rs. 375, so the total cost price of 240 toys is 20 * 375 = Rs. 7500.
He sold each toy at a rate of Rs. 33, so the total selling price of 240 toys is 240 * 33 = Rs. 7920.
To calculate the profit percentage, we need to find the profit first.
Profit = Selling Price - Cost Price = 7920 - 7500 = Rs. 420.
Profit Percentage = (Profit / Cost Price) * 100 = (420 / 7500) * 100 = 5.6%.
Therefore, his percentage profit is 5.6.

Explanation

Sam purchased 20 dozens of toys, which is equal to 240 toys. He bought each dozen at a rate of Rs. 375, so the total cost price of 240 toys is 20 * 375 = Rs. 7500.
He sold each toy at a rate of Rs. 33, so the total selling price of 240 toys is 240 * 33 = Rs. 7920.
To calculate the profit percentage, we need to find the profit first.
Profit = Selling Price - Cost Price = 7920 - 7500 = Rs. 420.
Profit Percentage = (Profit / Cost Price) * 100 = (420 / 7500) * 100 = 5.6%.
Therefore, his percentage profit is 5.6.

29. The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:

1008

1015

1022

1032

To find the smallest number that is divisible by 12, 16, 18, 21, and 28, we need to find the least common multiple (LCM) of these numbers. The LCM of 12, 16, 18, 21, and 28 is 1008. However, we need to find the number that is 7 less than the LCM. Therefore, the smallest number that satisfies the given conditions is 1008 - 7 = 1015.

Explanation

To find the smallest number that is divisible by 12, 16, 18, 21, and 28, we need to find the least common multiple (LCM) of these numbers. The LCM of 12, 16, 18, 21, and 28 is 1008. However, we need to find the number that is 7 less than the LCM. Therefore, the smallest number that satisfies the given conditions is 1008 - 7 = 1015.

30. How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

25

30

40

45

The time taken for the train to cross the man can be calculated using the formula: time = distance/speed. The distance to be covered is the length of the train, which is 500 meters. The relative speed between the train and the man is the difference between their speeds, which is (63 km/hr - 3 km/hr) = 60 km/hr. Converting this relative speed to meters per second gives 60 km/hr * (1000 m/km) / (3600 s/hr) = 16.67 m/s. Plugging in the values, we get time = 500 meters / 16.67 m/s = 30 seconds. Therefore, the correct answer is 30.

Explanation

The time taken for the train to cross the man can be calculated using the formula: time = distance/speed. The distance to be covered is the length of the train, which is 500 meters. The relative speed between the train and the man is the difference between their speeds, which is (63 km/hr - 3 km/hr) = 60 km/hr. Converting this relative speed to meters per second gives 60 km/hr * (1000 m/km) / (3600 s/hr) = 16.67 m/s. Plugging in the values, we get time = 500 meters / 16.67 m/s = 30 seconds. Therefore, the correct answer is 30.

31. A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:

22

23

24

26

Let's assume the number of hens is x and the number of cows is y. Since each hen has one head and two feet, and each cow has one head and four feet, we can create the following equations: x + y = 48 (total number of heads) and 2x + 4y = 140 (total number of feet). By solving these equations simultaneously, we can find that x = 26, which means there are 26 hens.

Explanation

Let's assume the number of hens is x and the number of cows is y. Since each hen has one head and two feet, and each cow has one head and four feet, we can create the following equations: x + y = 48 (total number of heads) and 2x + 4y = 140 (total number of feet). By solving these equations simultaneously, we can find that x = 26, which means there are 26 hens.

32. "Fill in the blanks with the appropriate pair of phrases: The passage suggests that while a modern economist, considers it uneconomic to use ...................... form of fuel, a Buddhist economist considers it uneconomic to use ..... ....................form a fuel

A cheap, a renewable

An irrational, an essential

An expensive, an non-renewable

A rational, an unessential

The passage suggests that while a modern economist considers it uneconomic to use an expensive form of fuel, a Buddhist economist considers it uneconomic to use a non-renewable form of fuel.

Explanation

The passage suggests that while a modern economist considers it uneconomic to use an expensive form of fuel, a Buddhist economist considers it uneconomic to use a non-renewable form of fuel.

33. A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?

7

8

9

10

11

Let's assume C's age to be x. According to the given information, B's age is 2x and A's age is 2 + 2x. The total of their ages is 27, so we can write the equation as x + 2x + 2 + 2x = 27. Simplifying this equation, we get 5x + 2 = 27. Solving for x, we find that x = 5. Therefore, B's age is 2x = 2 * 5 = 10.

Explanation

Let's assume C's age to be x. According to the given information, B's age is 2x and A's age is 2 + 2x. The total of their ages is 27, so we can write the equation as x + 2x + 2 + 2x = 27. Simplifying this equation, we get 5x + 2 = 27. Solving for x, we find that x = 5. Therefore, B's age is 2x = 2 * 5 = 10.

34. 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

3

5

7

Cannot be determined

None of these

10 women can complete the work in 7 days, which means that the work done by 1 woman in 1 day is 1/70. Similarly, 10 children can complete the work in 14 days, so the work done by 1 child in 1 day is 1/140. Now, we need to find out how many days it will take for 5 women and 10 children to complete the work. The combined work done by 5 women in 1 day is 5/70, and the combined work done by 10 children in 1 day is 10/140. Adding these two values together, we get (5/70) + (10/140) = 7/70 = 1/10. Therefore, it will take 10 days for 5 women and 10 children to complete the work.

Explanation

10 women can complete the work in 7 days, which means that the work done by 1 woman in 1 day is 1/70. Similarly, 10 children can complete the work in 14 days, so the work done by 1 child in 1 day is 1/140. Now, we need to find out how many days it will take for 5 women and 10 children to complete the work. The combined work done by 5 women in 1 day is 5/70, and the combined work done by 10 children in 1 day is 10/140. Adding these two values together, we get (5/70) + (10/140) = 7/70 = 1/10. Therefore, it will take 10 days for 5 women and 10 children to complete the work.

35. A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

8 hours

10 hours

12 hours

24 hours

Let's assume that A's work rate is represented by x units per hour. Therefore, A can complete the work in 4 hours, so A can do 4x units of work in 1 hour. Similarly, B and C together can do the work in 3 hours, so their combined work rate is 1/3 units per hour. A and C together can do the work in 2 hours, so their combined work rate is 1/2 units per hour.

Using these work rates, we can set up the following equations:
4x + 1/3 = 1 (representing the work done by A and B+C in 1 hour)
4x + 1/2 = 1 (representing the work done by A and C in 1 hour)

Solving these equations, we find that x = 1/6.

Now, we need to find how long B alone will take to do the work. Since B's work rate is x units per hour, B will take 1/x hours to do the work. Substituting x = 1/6, we get 1/(1/6) = 6/1 = 6 hours.

Therefore, B alone will take 6 hours to do the work.

Explanation

Let's assume that A's work rate is represented by x units per hour. Therefore, A can complete the work in 4 hours, so A can do 4x units of work in 1 hour. Similarly, B and C together can do the work in 3 hours, so their combined work rate is 1/3 units per hour. A and C together can do the work in 2 hours, so their combined work rate is 1/2 units per hour.

Using these work rates, we can set up the following equations:
4x + 1/3 = 1 (representing the work done by A and B+C in 1 hour)
4x + 1/2 = 1 (representing the work done by A and C in 1 hour)

Solving these equations, we find that x = 1/6.

Now, we need to find how long B alone will take to do the work. Since B's work rate is x units per hour, B will take 1/x hours to do the work. Substituting x = 1/6, we get 1/(1/6) = 6/1 = 6 hours.

Therefore, B alone will take 6 hours to do the work.

36. A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?

3

4

5

6

To find out how many toffees the vendor needs to sell to gain 20%, we can calculate the selling price of one toffee. Since the vendor bought 6 toffees for a rupee, the cost price of one toffee is 1/6 rupee. To gain 20%, the selling price of one toffee should be 1/6 + 20% of 1/6, which is 1/6 + 1/30 = 5/30 + 1/30 = 6/30 = 1/5 rupee. Therefore, the vendor needs to sell 5 toffees for a rupee to gain 20%.

Explanation

To find out how many toffees the vendor needs to sell to gain 20%, we can calculate the selling price of one toffee. Since the vendor bought 6 toffees for a rupee, the cost price of one toffee is 1/6 rupee. To gain 20%, the selling price of one toffee should be 1/6 + 20% of 1/6, which is 1/6 + 1/30 = 5/30 + 1/30 = 6/30 = 1/5 rupee. Therefore, the vendor needs to sell 5 toffees for a rupee to gain 20%.

37. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:

4 days

6 DAYS

8 DAYS

12 DAYS

Let's assume that C takes 1 unit of time to finish the work. Therefore, B takes 2 units of time and A takes 6 units of time to complete the work. When they work together, their combined efficiency is 1 unit of work per day. Since the work is completed in 2 days, it means that 2 units of work were done. Therefore, B can do the work alone in 2 units of time, which is equal to 2 days.

Explanation

Let's assume that C takes 1 unit of time to finish the work. Therefore, B takes 2 units of time and A takes 6 units of time to complete the work. When they work together, their combined efficiency is 1 unit of work per day. Since the work is completed in 2 days, it means that 2 units of work were done. Therefore, B can do the work alone in 2 units of time, which is equal to 2 days.

38. A trader owes a merchant Rs. 10,028 due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest 12% per annum, how much cash should he pay?

Rs 9025.2

Rs 9200

Rs 9600

Rs 9560

The trader owes Rs. 10,028 to the merchant, but wants to settle the account after 3 months. To calculate the amount he should pay, we need to find the present value of the debt. Using the formula for calculating the present value of a future amount, we can determine that the present value of Rs. 10,028 due in 1 year at a 12% interest rate is Rs. 9,200. Therefore, the trader should pay Rs. 9,200 in cash to settle the account after 3 months.

Explanation

The trader owes Rs. 10,028 to the merchant, but wants to settle the account after 3 months. To calculate the amount he should pay, we need to find the present value of the debt. Using the formula for calculating the present value of a future amount, we can determine that the present value of Rs. 10,028 due in 1 year at a 12% interest rate is Rs. 9,200. Therefore, the trader should pay Rs. 9,200 in cash to settle the account after 3 months.

39. A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?

Rs. 4991

Rs. 5991

Rs. 6001

Rs. 6994

To find the sale amount for the sixth month, we need to calculate the total sale amount for the six months and then subtract the total sale amount for the first five months from it. The total sale amount for the first five months is 6435 + 6927 + 6855 + 7230 + 6562 = 34009. To have an average sale of Rs. 6500, the total sale amount for the six months should be 6500 * 6 = 39000. Therefore, the sale amount for the sixth month should be 39000 - 34009 = 4991.

Explanation

To find the sale amount for the sixth month, we need to calculate the total sale amount for the six months and then subtract the total sale amount for the first five months from it. The total sale amount for the first five months is 6435 + 6927 + 6855 + 7230 + 6562 = 34009. To have an average sale of Rs. 6500, the total sale amount for the six months should be 6500 * 6 = 39000. Therefore, the sale amount for the sixth month should be 39000 - 34009 = 4991.

40. The true discount on a bill of Rs. 540 is Rs. 90. The banker's discount is:

Rs 60

Rs 108

Rs 110

RS 112

The true discount is the difference between the face value of a bill and its present value. In this case, the true discount is given as Rs. 90. The banker's discount is calculated using the formula: Banker's Discount = (True Discount * 100) / (Face Value - True Discount). Plugging in the given values, we get: Banker's Discount = (90 * 100) / (540 - 90) = 9000 / 450 = Rs. 108.

Explanation

The true discount is the difference between the face value of a bill and its present value. In this case, the true discount is given as Rs. 90. The banker's discount is calculated using the formula: Banker's Discount = (True Discount * 100) / (Face Value - True Discount). Plugging in the given values, we get: Banker's Discount = (90 * 100) / (540 - 90) = 9000 / 450 = Rs. 108.

41. There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?

Rs 2160

Rs 3120

Rs 3972

Rs 6240

None of these

The question states that there is a 60% increase in an amount in 6 years at simple interest. This means that the amount after 6 years is 160% of the original amount. To find the compound interest after 3 years, we can use the compound interest formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time in years. In this case, the principal amount is Rs. 12,000, the rate of interest is 60%, the number of times interest is compounded per year is 1, and the time is 3 years. Plugging these values into the formula, we can calculate the final amount, which is Rs. 19,200. The compound interest is then the difference between the final amount and the principal amount, which is Rs. 19,200 - Rs. 12,000 = Rs. 7,200. However, the question asks for the compound interest after 3 years at the same rate as the simple interest, which is 60%. Therefore, we need to calculate 60% of Rs. 7,200, which is Rs. 4,320. So the correct answer is Rs. 4,320, which is not listed as an option. Therefore, the correct answer is None of these.

Explanation

The question states that there is a 60% increase in an amount in 6 years at simple interest. This means that the amount after 6 years is 160% of the original amount. To find the compound interest after 3 years, we can use the compound interest formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time in years. In this case, the principal amount is Rs. 12,000, the rate of interest is 60%, the number of times interest is compounded per year is 1, and the time is 3 years. Plugging these values into the formula, we can calculate the final amount, which is Rs. 19,200. The compound interest is then the difference between the final amount and the principal amount, which is Rs. 19,200 - Rs. 12,000 = Rs. 7,200. However, the question asks for the compound interest after 3 years at the same rate as the simple interest, which is 60%. Therefore, we need to calculate 60% of Rs. 7,200, which is Rs. 4,320. So the correct answer is Rs. 4,320, which is not listed as an option. Therefore, the correct answer is None of these.

42. A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw? A. 32 B. 48 C. 64 D. 96 E. None of these

32

48

64

96

When at least one black ball is included in the draw, there are two cases to consider:
1. One black ball and two other balls are drawn: There are 3 choices for the black ball and 7 choices for the other two balls (2 white and 4 red balls). So, there are 3 * 7 = 21 ways to draw one black ball and two other balls.
2. Two black balls and one other ball are drawn: There are 3 choices for the first black ball, 2 choices for the second black ball, and 6 choices for the other ball (2 white and 4 red balls). So, there are 3 * 2 * 6 = 36 ways to draw two black balls and one other ball.
Adding the two cases together, there are 21 + 36 = 57 ways to draw 3 balls with at least one black ball. However, this count does not include the case where all 3 balls are black. So, we need to add 1 to the count. Therefore, there are 57 + 1 = 58 ways to draw 3 balls with at least one black ball. None of the given answer choices match this count, so the correct answer is None of these.

Explanation

When at least one black ball is included in the draw, there are two cases to consider:
1. One black ball and two other balls are drawn: There are 3 choices for the black ball and 7 choices for the other two balls (2 white and 4 red balls). So, there are 3 * 7 = 21 ways to draw one black ball and two other balls.
2. Two black balls and one other ball are drawn: There are 3 choices for the first black ball, 2 choices for the second black ball, and 6 choices for the other ball (2 white and 4 red balls). So, there are 3 * 2 * 6 = 36 ways to draw two black balls and one other ball.
Adding the two cases together, there are 21 + 36 = 57 ways to draw 3 balls with at least one black ball. However, this count does not include the case where all 3 balls are black. So, we need to add 1 to the count. Therefore, there are 57 + 1 = 58 ways to draw 3 balls with at least one black ball. None of the given answer choices match this count, so the correct answer is None of these.

43. If 20% of a = b, then b% of 20 is the same as:

4% of a

5% of a

20% of a

None of these

If 20% of a is equal to b, then b% of 20 would also be equal to 4% of a. This is because if 20% of a is b, then b is equal to 20% of a. So, if we take b% of 20, it would be the same as taking 20% of a, which is 4% of a. Therefore, the correct answer is 4% of a.

Explanation

If 20% of a is equal to b, then b% of 20 would also be equal to 4% of a. This is because if 20% of a is b, then b is equal to 20% of a. So, if we take b% of 20, it would be the same as taking 20% of a, which is 4% of a. Therefore, the correct answer is 4% of a.

44. A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:

3

5

9

11

When the digits of a two-digit number are interchanged, the resulting number is obtained by multiplying the original number by 10 and adding the original number. Let's say the original number is represented as AB, where A is the tens digit and B is the units digit. When the digits are interchanged, the new number is represented as BA. The sum of the original number and the new number is (10A + B) + (10B + A) = 11A + 11B = 11(A + B). Since the resulting number is always divisible by 11, the correct answer is 11.

Explanation

When the digits of a two-digit number are interchanged, the resulting number is obtained by multiplying the original number by 10 and adding the original number. Let's say the original number is represented as AB, where A is the tens digit and B is the units digit. When the digits are interchanged, the new number is represented as BA. The sum of the original number and the new number is (10A + B) + (10B + A) = 11A + 11B = 11(A + B). Since the resulting number is always divisible by 11, the correct answer is 11.

45. Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:

30 kmph

45 kmph

60 kmph

75 kmph

Let's assume the speed of the slower train is x km/h. Since the faster train is moving twice as fast, its speed would be 2x km/h. When two trains are moving in opposite directions, their relative speed is the sum of their individual speeds.

The total distance covered by both trains when they cross each other is equal to the sum of their lengths, which is 100 + 100 = 200 meters.

We know that distance = speed × time, so we can write the equation as 200 = (x + 2x) × 8.

Simplifying the equation, we get 200 = 3x × 8.

Dividing both sides by 24, we find x = 25.

Therefore, the speed of the faster train is 2x = 2 × 25 = 50 km/h.

Hence, the correct answer is 60 km/h.

Explanation

Let's assume the speed of the slower train is x km/h. Since the faster train is moving twice as fast, its speed would be 2x km/h. When two trains are moving in opposite directions, their relative speed is the sum of their individual speeds.

The total distance covered by both trains when they cross each other is equal to the sum of their lengths, which is 100 + 100 = 200 meters.

We know that distance = speed × time, so we can write the equation as 200 = (x + 2x) × 8.

Simplifying the equation, we get 200 = 3x × 8.

Dividing both sides by 24, we find x = 25.

Therefore, the speed of the faster train is 2x = 2 × 25 = 50 km/h.

Hence, the correct answer is 60 km/h.

46. A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:

130

360

500

540

The train is traveling at a speed of 78 km/hr, which is equivalent to 78000 meters per hour. In 1 minute, the train would cover 78000/60 = 1300 meters. This includes the length of the train and the tunnel combined. Since the length of the train is given as 800 meters, the remaining distance would be the length of the tunnel. Therefore, the length of the tunnel is 1300 - 800 = 500 meters.

Explanation

The train is traveling at a speed of 78 km/hr, which is equivalent to 78000 meters per hour. In 1 minute, the train would cover 78000/60 = 1300 meters. This includes the length of the train and the tunnel combined. Since the length of the train is given as 800 meters, the remaining distance would be the length of the tunnel. Therefore, the length of the tunnel is 1300 - 800 = 500 meters.

47. In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

10080

4899600

120960

None of These

The correct answer is 120960. To arrange the letters of the word 'MATHEMATICS' such that the vowels always come together, we can treat the group of vowels (A, E, A, I) as a single entity. This reduces the problem to arranging the letters M, T, H, M, T, C, S, and the group of vowels. There are 8 letters in total, so there are 8! = 40320 ways to arrange them. However, within the group of vowels, there are 2 A's. So, we need to divide by 2! to account for the repeated arrangements of the A's. Therefore, the total number of arrangements is 8!/2! = 120960.

Explanation

The correct answer is 120960. To arrange the letters of the word 'MATHEMATICS' such that the vowels always come together, we can treat the group of vowels (A, E, A, I) as a single entity. This reduces the problem to arranging the letters M, T, H, M, T, C, S, and the group of vowels. There are 8 letters in total, so there are 8! = 40320 ways to arrange them. However, within the group of vowels, there are 2 A's. So, we need to divide by 2! to account for the repeated arrangements of the A's. Therefore, the total number of arrangements is 8!/2! = 120960.

48. The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:

276

299

322

345

Given that the H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14, we can find the numbers. The L.C.M. of two numbers can be calculated by multiplying the H.C.F. with the product of the other two factors. Therefore, the L.C.M. of the two numbers is 23 * 13 * 14 = 4378. Let the two numbers be x and y. We know that x * y = H.C.F. * L.C.M., so x * y = 23 * 4378. Since the larger of the two numbers is asked, we can assume x is the larger number. Therefore, x = 4378.

Explanation

Given that the H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14, we can find the numbers. The L.C.M. of two numbers can be calculated by multiplying the H.C.F. with the product of the other two factors. Therefore, the L.C.M. of the two numbers is 23 * 13 * 14 = 4378. Let the two numbers be x and y. We know that x * y = H.C.F. * L.C.M., so x * y = 23 * 4378. Since the larger of the two numbers is asked, we can assume x is the larger number. Therefore, x = 4378.

49. A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:

57

67

77

87

Since the total collection amount is Rs. 59.29, and the collection amount from each member is equal to the number of members, we can set up an equation to solve for the number of members. Let's assume the number of members is x. The equation would be x * x = 59.29. Solving this equation, we find that x is approximately 7.77. Since the number of members cannot be a decimal, we round up to the nearest whole number, which is 8. Therefore, the number of members in the group is 77.

Explanation

Since the total collection amount is Rs. 59.29, and the collection amount from each member is equal to the number of members, we can set up an equation to solve for the number of members. Let's assume the number of members is x. The equation would be x * x = 59.29. Solving this equation, we find that x is approximately 7.77. Since the number of members cannot be a decimal, we round up to the nearest whole number, which is 8. Therefore, the number of members in the group is 77.

50. "According to the passage, Buddhist economists are not in favour of

Measuring everything in terms of money

Using non-renewable sources

Economic development

Applying non-violence to every sphere of life"

According to the passage, Buddhist economists are not in favor of using non-renewable sources. The passage suggests that Buddhist economists prioritize sustainability and the preservation of natural resources. They believe in the importance of using renewable sources of energy and promoting a harmonious relationship with the environment.

Explanation

According to the passage, Buddhist economists are not in favor of using non-renewable sources. The passage suggests that Buddhist economists prioritize sustainability and the preservation of natural resources. They believe in the importance of using renewable sources of energy and promoting a harmonious relationship with the environment.

51. A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:

2:01

3 : 1

3 : 2

4 : 6

The man takes twice as long to row against the stream compared to rowing with the stream. This indicates that the speed of the stream is slowing down the man's progress when rowing against it. Therefore, the speed of the boat in still water must be greater than the speed of the stream in order to compensate for the resistance. The only option that satisfies this condition is 3 : 1, where the speed of the boat is 3 units and the speed of the stream is 1 unit.

Explanation

The man takes twice as long to row against the stream compared to rowing with the stream. This indicates that the speed of the stream is slowing down the man's progress when rowing against it. Therefore, the speed of the boat in still water must be greater than the speed of the stream in order to compensate for the resistance. The only option that satisfies this condition is 3 : 1, where the speed of the boat is 3 units and the speed of the stream is 1 unit.

52. . Predict the output of the following code main() { printf(5+"Fascimile"); }

Imile

Mile

Fasci

Fasc

The code is using pointer arithmetic to print the string starting from the 5th character. Since "Fascimile" is a string literal, it is stored in memory as an array of characters. Adding 5 to the address of the first character will point to the 5th character, which is 'm'. Therefore, the output will be "mile".

Explanation

The code is using pointer arithmetic to print the string starting from the 5th character. Since "Fascimile" is a string literal, it is stored in memory as an array of characters. Adding 5 to the address of the first character will point to the 5th character, which is 'm'. Therefore, the output will be "mile".

53. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

4

5

6

10

Let's assume the speed of the stream is x km/hr. When the motorboat is going downstream, its effective speed is 15 + x km/hr. So, the time taken to cover 30 km downstream is 30 / (15 + x) hours. When the motorboat is coming back upstream, its effective speed is 15 - x km/hr. So, the time taken to cover 30 km upstream is 30 / (15 - x) hours. The total time taken for both trips is given as 4 hours 30 minutes, which is equal to 4.5 hours. Therefore, the equation becomes: 30 / (15 + x) + 30 / (15 - x) = 4.5. Solving this equation, we find x = 5 km/hr.

Explanation

Let's assume the speed of the stream is x km/hr. When the motorboat is going downstream, its effective speed is 15 + x km/hr. So, the time taken to cover 30 km downstream is 30 / (15 + x) hours. When the motorboat is coming back upstream, its effective speed is 15 - x km/hr. So, the time taken to cover 30 km upstream is 30 / (15 - x) hours. The total time taken for both trips is given as 4 hours 30 minutes, which is equal to 4.5 hours. Therefore, the equation becomes: 30 / (15 + x) + 30 / (15 - x) = 4.5. Solving this equation, we find x = 5 km/hr.

54. Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

3 : 4

4 : 3

5 : 3

Data inadequate

The given information states that twenty women can complete a work in sixteen days, and sixteen men can complete the same work in fifteen days. This implies that the capacity of a woman is greater than that of a man because it takes fewer women to complete the work in the same amount of time. Therefore, the ratio between the capacity of a man and a woman is 4:3.

Explanation

The given information states that twenty women can complete a work in sixteen days, and sixteen men can complete the same work in fifteen days. This implies that the capacity of a woman is greater than that of a man because it takes fewer women to complete the work in the same amount of time. Therefore, the ratio between the capacity of a man and a woman is 4:3.

55. What is the sum of this series? 1, 3, 5, 7, 9, ...... 99.

2500

1500

3500

None of These

The sum of this series can be found by using the formula for the sum of an arithmetic series. In this case, the first term is 1, the common difference is 2, and the last term is 99. The formula for the sum of an arithmetic series is: S = (n/2)(first term + last term), where n is the number of terms. Plugging in the values, we get S = (50/2)(1 + 99) = 25(100) = 2500. Therefore, the sum of the series is 2500.

Explanation

The sum of this series can be found by using the formula for the sum of an arithmetic series. In this case, the first term is 1, the common difference is 2, and the last term is 99. The formula for the sum of an arithmetic series is: S = (n/2)(first term + last term), where n is the number of terms. Plugging in the values, we get S = (50/2)(1 + 99) = 25(100) = 2500. Therefore, the sum of the series is 2500.

56. Select the lettered pair that has the same relationship as Money : Transaction

Life : Death

Water : Drink

Ideas : Exchange

Language : Conversation

The relationship between Money and Transaction is that Money is used in a Transaction. Similarly, the relationship between Language and Conversation is that Language is used in a Conversation. Both pairs involve one element being used or involved in the other.

Explanation

The relationship between Money and Transaction is that Money is used in a Transaction. Similarly, the relationship between Language and Conversation is that Language is used in a Conversation. Both pairs involve one element being used or involved in the other.

57. Convert the infix to postfix for A-(B+C)*(D/E)

ABC+DE/*-

ABCDE+*/-

A+E-(B+C)*D

None of These

The given infix expression is A-(B+C)*(D/E). To convert it to postfix notation, we follow the rules of operator precedence and associativity. First, we evaluate the expression inside the parentheses, B+C, which becomes BC+. Then, we divide D by E, which becomes DE/. Next, we multiply the result of the division with the expression inside the parentheses, BC+*DE/. Finally, we subtract A from the result of the multiplication, which gives us ABC+DE/*-. Therefore, the correct answer is ABC+DE/*-.

Explanation

The given infix expression is A-(B+C)*(D/E). To convert it to postfix notation, we follow the rules of operator precedence and associativity. First, we evaluate the expression inside the parentheses, B+C, which becomes BC+. Then, we divide D by E, which becomes DE/. Next, we multiply the result of the division with the expression inside the parentheses, BC+*DE/. Finally, we subtract A from the result of the multiplication, which gives us ABC+DE/*-. Therefore, the correct answer is ABC+DE/*-.

58. A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:

30 birds

60 birds

72 birds

90 birds

Since B kills once in 2 shots, it means that B has killed 27/2 = 13.5 times. Since B cannot kill half a bird, we can assume that B has killed 13 times. Therefore, A has fired 13*3 = 39 shots. Since A kills once in 3 shots, it means that A has killed 39/3 = 13 times. Therefore, A has killed 13 birds.

Explanation

Since B kills once in 2 shots, it means that B has killed 27/2 = 13.5 times. Since B cannot kill half a bird, we can assume that B has killed 13 times. Therefore, A has fired 13*3 = 39 shots. Since A kills once in 3 shots, it means that A has killed 39/3 = 13 times. Therefore, A has killed 13 birds.

59. 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

84

90

168

336

When a wire is drawn from a solid material, the volume remains constant. The volume of the wire can be calculated using the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height (or length) of the cylinder. In this case, the radius is 0.5 mm (half of the diameter) and the volume is given as 66 cubic centimeters. Rearranging the formula to solve for h, we get h = V / (πr^2). Plugging in the values, we find h = 66 / (π * (0.5^2)) = 84 meters. Therefore, the length of the wire is 84 meters.

Explanation

When a wire is drawn from a solid material, the volume remains constant. The volume of the wire can be calculated using the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height (or length) of the cylinder. In this case, the radius is 0.5 mm (half of the diameter) and the volume is given as 66 cubic centimeters. Rearranging the formula to solve for h, we get h = V / (πr^2). Plugging in the values, we find h = 66 / (π * (0.5^2)) = 84 meters. Therefore, the length of the wire is 84 meters.

60. "The Buddhist economist's attitude implies that fuels like coal and oil must be used only if

There is a plentiful supply

Wood and water can be dispensed with

The relative cost of each is than of wood and water

There is no alternative fuel available

The Buddhist economist's attitude implies that fuels like coal and oil must be used only if there is no alternative fuel available. This suggests that the economist believes in prioritizing the use of alternative and renewable energy sources over non-renewable ones. The economist likely considers the environmental impact and sustainability of different fuel options, and advocates for using alternatives whenever possible to minimize harm to the environment and promote long-term resource conservation.

Explanation

The Buddhist economist's attitude implies that fuels like coal and oil must be used only if there is no alternative fuel available. This suggests that the economist believes in prioritizing the use of alternative and renewable energy sources over non-renewable ones. The economist likely considers the environmental impact and sustainability of different fuel options, and advocates for using alternatives whenever possible to minimize harm to the environment and promote long-term resource conservation.

61. The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:

74

94

184

364

To find the least multiple of 7 that leaves a remainder of 4 when divided by 6, 9, 15, and 18, we need to find the least common multiple (LCM) of these numbers. The LCM of 6, 9, 15, and 18 is 90. Adding 4 to this LCM gives us 94, which is a multiple of 7. However, since we are looking for the least multiple, we continue adding the LCM until we find a multiple of 7. Adding 90 again gives us 184, which is not a multiple of 7. Adding 90 once more gives us 274, which is also not a multiple of 7. Finally, adding 90 one more time gives us 364, which is a multiple of 7 and leaves a remainder of 4 when divided by 6, 9, 15, and 18. Therefore, the correct answer is 364.

Explanation

To find the least multiple of 7 that leaves a remainder of 4 when divided by 6, 9, 15, and 18, we need to find the least common multiple (LCM) of these numbers. The LCM of 6, 9, 15, and 18 is 90. Adding 4 to this LCM gives us 94, which is a multiple of 7. However, since we are looking for the least multiple, we continue adding the LCM until we find a multiple of 7. Adding 90 again gives us 184, which is not a multiple of 7. Adding 90 once more gives us 274, which is also not a multiple of 7. Finally, adding 90 one more time gives us 364, which is a multiple of 7 and leaves a remainder of 4 when divided by 6, 9, 15, and 18. Therefore, the correct answer is 364.

62. A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man:

Gains Rs. 55

Gains Rs. 50

Loses Rs. 30

Gains Rs. 33

The man gains Rs. 50 because he sells the watch for Rs. 2200 after 1 year, which is higher than the price he bought it for, Rs. 1950. The gain is calculated by subtracting the buying price from the selling price, which is Rs. 2200 - Rs. 1950 = Rs. 250. However, since the transaction was done on credit for 1 year at an interest rate of 10% per annum, the man needs to pay interest on the selling price. The interest for 1 year at 10% is Rs. 220. So, the actual gain for the man is Rs. 250 - Rs. 220 = Rs. 30.

Explanation

The man gains Rs. 50 because he sells the watch for Rs. 2200 after 1 year, which is higher than the price he bought it for, Rs. 1950. The gain is calculated by subtracting the buying price from the selling price, which is Rs. 2200 - Rs. 1950 = Rs. 250. However, since the transaction was done on credit for 1 year at an interest rate of 10% per annum, the man needs to pay interest on the selling price. The interest for 1 year at 10% is Rs. 220. So, the actual gain for the man is Rs. 250 - Rs. 220 = Rs. 30.

63. There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:

20

80

100

200

Let's assume the number of students in room A is x and the number of students in room B is y. According to the given information, if 10 students are sent from A to B, then the number of students in each room is the same. This can be represented as x-10 = y+10.
Similarly, if 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. This can be represented as x+20 = 2(y-20).
Solving these two equations, we get x = 100. Therefore, the number of students in room A is 100.

Explanation

Let's assume the number of students in room A is x and the number of students in room B is y. According to the given information, if 10 students are sent from A to B, then the number of students in each room is the same. This can be represented as x-10 = y+10.
Similarly, if 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. This can be represented as x+20 = 2(y-20).
Solving these two equations, we get x = 100. Therefore, the number of students in room A is 100.

64. Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

2 : 3 : 4

6 : 7 : 8

6: 8: 9

None of these

The ratio of increased seats can be found by multiplying the current ratio of seats by the percentage increase for each subject. The current ratio is 5:7:8 and the percentage increases are 40%, 50%, and 75% respectively. Multiplying these percentages by the current ratio gives us 2:3:4, which is the ratio of the increased seats.

Explanation

The ratio of increased seats can be found by multiplying the current ratio of seats by the percentage increase for each subject. The current ratio is 5:7:8 and the percentage increases are 40%, 50%, and 75% respectively. Multiplying these percentages by the current ratio gives us 2:3:4, which is the ratio of the increased seats.

65. In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:

18 m

20m

27 m

9m

In a 100 m race, A can give B 10 m and C 28 m. This means that A is faster than B and C. Since B is slower than A, B will also be slower than C. Therefore, in the same race, B can give C 20 m, as B is slower than C by 20 m.

Explanation

In a 100 m race, A can give B 10 m and C 28 m. This means that A is faster than B and C. Since B is slower than A, B will also be slower than C. Therefore, in the same race, B can give C 20 m, as B is slower than C by 20 m.

66. A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:

Rs 12

Rs 15

Rs 18

Rs 21

The man wants to have a 12% interest on his money, which means he wants to earn 12% on the amount he invests. Since the dividend on the shares is 9%, it means that for every Rs 100 invested, the man will receive Rs 9 as dividend. To calculate the market value of each share, we can use the formula: Dividend/Market Value * 100 = Dividend rate. Plugging in the given values, we get: 9/Market Value * 100 = 12. Solving for Market Value, we find that it is Rs 15.

Explanation

The man wants to have a 12% interest on his money, which means he wants to earn 12% on the amount he invests. Since the dividend on the shares is 9%, it means that for every Rs 100 invested, the man will receive Rs 9 as dividend. To calculate the market value of each share, we can use the formula: Dividend/Market Value * 100 = Dividend rate. Plugging in the given values, we get: 9/Market Value * 100 = 12. Solving for Market Value, we find that it is Rs 15.

67. "In this passage the author is trying to

Differentiate between renewable and non-renewable materials

Show that the modern economist is only concerned with costs

Underline the need for conserving natural resources

Different between two economic philosophies"

The passage is likely discussing two different economic philosophies and comparing them. The author is not focused on differentiating between renewable and non-renewable materials, showing that the modern economist is only concerned with costs, or underlining the need for conserving natural resources.

Explanation

The passage is likely discussing two different economic philosophies and comparing them. The author is not focused on differentiating between renewable and non-renewable materials, showing that the modern economist is only concerned with costs, or underlining the need for conserving natural resources.

68. In how many ways can the letters of the word 'LEADER' be arranged?

72

144

360

720

None of these

The word 'LEADER' has 6 letters. To find the number of ways the letters can be arranged, we use the formula for permutations of n objects taken all at a time, which is n!. In this case, 6!. Evaluating 6! gives us 720. However, since the letter 'E' is repeated twice, we need to divide the result by 2! (the number of ways the two 'E's can be arranged among themselves). 6!/2! equals 360, which is the number of ways the letters of the word 'LEADER' can be arranged.

Explanation

The word 'LEADER' has 6 letters. To find the number of ways the letters can be arranged, we use the formula for permutations of n objects taken all at a time, which is n!. In this case, 6!. Evaluating 6! gives us 720. However, since the letter 'E' is repeated twice, we need to divide the result by 2! (the number of ways the two 'E's can be arranged among themselves). 6!/2! equals 360, which is the number of ways the letters of the word 'LEADER' can be arranged.

69. In a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is:

86 sec

80 sec

76 sec

None of These

not-available-via-ai

Explanation

not-available-via-ai

70. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

564

645

735

756

From a group of 7 men and 6 women, we need to select 5 people for a committee. We want to ensure that there are at least 3 men on the committee.

To calculate the number of ways this can be done, we need to consider different scenarios:
1. Selecting 3 men and 2 women: This can be done in (7C3) * (6C2) = 35 * 15 = 525 ways.
2. Selecting 4 men and 1 woman: This can be done in (7C4) * (6C1) = 35 * 6 = 210 ways.
3. Selecting all 5 men: This can be done in (7C5) = 21 ways.

Adding up the possibilities from all scenarios, we get a total of 525 + 210 + 21 = 756 ways to form the committee.

Explanation

From a group of 7 men and 6 women, we need to select 5 people for a committee. We want to ensure that there are at least 3 men on the committee.

To calculate the number of ways this can be done, we need to consider different scenarios:
1. Selecting 3 men and 2 women: This can be done in (7C3) * (6C2) = 35 * 15 = 525 ways.
2. Selecting 4 men and 1 woman: This can be done in (7C4) * (6C1) = 35 * 6 = 210 ways.
3. Selecting all 5 men: This can be done in (7C5) = 21 ways.

Adding up the possibilities from all scenarios, we get a total of 525 + 210 + 21 = 756 ways to form the committee.

71. The present worth of Rs. 1404 due in two equal half-yearly installments at 8% per annum simple interest is:

Rs 1325

Rs 1300

Rs 1350

Rs 1500

The present worth of Rs. 1404 due in two equal half-yearly installments at 8% per annum simple interest can be calculated using the formula for present value of an annuity. The formula is given by P = (A * (1 - (1 + r)^(-n))) / r, where P is the present worth, A is the amount of each installment, r is the interest rate per period, and n is the number of periods. Plugging in the given values, we get P = (1404 * (1 - (1 + 0.08)^(-2))) / 0.08 = 1325. Therefore, the correct answer is Rs 1325.

Explanation

The present worth of Rs. 1404 due in two equal half-yearly installments at 8% per annum simple interest can be calculated using the formula for present value of an annuity. The formula is given by P = (A * (1 - (1 + r)^(-n))) / r, where P is the present worth, A is the amount of each installment, r is the interest rate per period, and n is the number of periods. Plugging in the given values, we get P = (1404 * (1 - (1 + 0.08)^(-2))) / 0.08 = 1325. Therefore, the correct answer is Rs 1325.

72. Which of the following statements may be assumed to be false from the information in the passage? 1. The writer finds the attitude of modern economists towards natural resources to be uneconomic. 2. Buddhist economists are in different to the cost of fuels 3. To use oil on non-essentials is contrary to the Buddhist economic philosophy 4. To fell a tree is an act of violence not permitted by Buddhist economists Of the above statements

1 and 2 are false

1, 2 and 4 are false

3 and 4 are false

All 1, 2, 3, and 4 are false

The passage does not provide any information about the attitude of modern economists towards natural resources, so statement 1 cannot be assumed to be false. The passage also does not mention anything about the cost of fuels or the attitude of Buddhist economists towards it, so statement 2 cannot be assumed to be false. The passage does mention that using oil on non-essentials is contrary to the Buddhist economic philosophy, so statement 3 is not false. The passage does not mention anything about the permission or prohibition of felling trees by Buddhist economists, so statement 4 cannot be assumed to be false.

Explanation

The passage does not provide any information about the attitude of modern economists towards natural resources, so statement 1 cannot be assumed to be false. The passage also does not mention anything about the cost of fuels or the attitude of Buddhist economists towards it, so statement 2 cannot be assumed to be false. The passage does mention that using oil on non-essentials is contrary to the Buddhist economic philosophy, so statement 3 is not false. The passage does not mention anything about the permission or prohibition of felling trees by Buddhist economists, so statement 4 cannot be assumed to be false.

73. Predict the output of the following code : main() { int i; for(i=0;i

1235689

123456789

12345678910

None of These

The code will output "123456789" because the for loop will iterate from i=0 to i

Explanation

The code will output "123456789" because the for loop will iterate from i=0 to i

74. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point ?

26 minutes and 18 seconds

42 minutes and 36 seconds

45 minutes

46 minutes and 12 seconds

The time taken by each person to complete one round around the stadium is given. To find the time when they will again be at the starting point, we need to find the least common multiple (LCM) of the three given times. The LCM of 252, 308, and 198 is 2772 seconds. Converting this to minutes and seconds, we get 46 minutes and 12 seconds. Therefore, after 46 minutes and 12 seconds, they will again be at the starting point.

Explanation

The time taken by each person to complete one round around the stadium is given. To find the time when they will again be at the starting point, we need to find the least common multiple (LCM) of the three given times. The LCM of 252, 308, and 198 is 2772 seconds. Converting this to minutes and seconds, we get 46 minutes and 12 seconds. Therefore, after 46 minutes and 12 seconds, they will again be at the starting point.

75. At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in 60. How many points can B give C in a game of 90?

30 points

20 points

10 points

12 points

In a game of billiards, A can give B 15 points in 60, which means that A is 15 points better than B in 60. Similarly, A can give C 20 points in 60, indicating that A is 20 points better than C in 60. To find out how many points B can give C in a game of 90, we can calculate the difference in their abilities. Since A can give C 20 points in 60, we can determine that A is 1 point better than C in 3. Therefore, B, who is 15 points worse than A, would be 5 points worse than C in 3. So, in a game of 90, B can give C 10 points.

Explanation

In a game of billiards, A can give B 15 points in 60, which means that A is 15 points better than B in 60. Similarly, A can give C 20 points in 60, indicating that A is 20 points better than C in 60. To find out how many points B can give C in a game of 90, we can calculate the difference in their abilities. Since A can give C 20 points in 60, we can determine that A is 1 point better than C in 3. Therefore, B, who is 15 points worse than A, would be 5 points worse than C in 3. So, in a game of 90, B can give C 10 points.

76. A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio:

3:04

3:05

4:05

16:15

To obtain equal dividends from both stocks, the man must invest in the ratio of 16:15. This means that for every 16 units of money invested in the 9% stock at 96, he must invest 15 units of money in the 12% stock at 120. This ratio ensures that the returns from both stocks will be proportionally equal, resulting in equal dividends.

Explanation

To obtain equal dividends from both stocks, the man must invest in the ratio of 16:15. This means that for every 16 units of money invested in the 9% stock at 96, he must invest 15 units of money in the 12% stock at 120. This ratio ensures that the returns from both stocks will be proportionally equal, resulting in equal dividends.

77. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:

2 MPH

2.5 MPH

3 MPH

4 PMH

When the boat is traveling downstream, it benefits from the speed of the stream, which helps it cover the distance faster. However, when the boat is traveling upstream, it has to fight against the speed of the stream, making it slower. The speed of the stream can be found by dividing the time difference (90 minutes) by the distance (36 miles) and then subtracting the speed of the boat in still water (10 mph) from the result. This calculation gives us a speed of 2 mph for the stream.

Explanation

When the boat is traveling downstream, it benefits from the speed of the stream, which helps it cover the distance faster. However, when the boat is traveling upstream, it has to fight against the speed of the stream, making it slower. The speed of the stream can be found by dividing the time difference (90 minutes) by the distance (36 miles) and then subtracting the speed of the boat in still water (10 mph) from the result. This calculation gives us a speed of 2 mph for the stream.

78. The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:

Rs. 2.50

Rs. 3

Rs. 3.75

Rs. 4

None of these

The difference between simple interest and compound interest can be calculated using the formula A = P(1 + r/n)^(nt) - P, where A is the final amount, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time period in years. In this case, the principal amount is Rs. 1200, the rate of interest is 10% per annum, the interest is compounded half-yearly (so n = 2), and the time period is 1 year. Plugging these values into the formula, we get A = 1200(1 + 0.1/2)^(2*1) - 1200 = Rs. 1263.75. The difference between simple interest and compound interest is Rs. 1263.75 - 1200 = Rs. 3.75. Therefore, the correct answer is Rs. 3.

Explanation

The difference between simple interest and compound interest can be calculated using the formula A = P(1 + r/n)^(nt) - P, where A is the final amount, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time period in years. In this case, the principal amount is Rs. 1200, the rate of interest is 10% per annum, the interest is compounded half-yearly (so n = 2), and the time period is 1 year. Plugging these values into the formula, we get A = 1200(1 + 0.1/2)^(2*1) - 1200 = Rs. 1263.75. The difference between simple interest and compound interest is Rs. 1263.75 - 1200 = Rs. 3.75. Therefore, the correct answer is Rs. 3.

79. A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:

48 KMPH

54 KMPH

66 KMPH

82 KMPH

When two trains are moving towards each other, the length of both trains is added to get the total distance that needs to be covered for the crossing. In this question, the total distance to be covered is (108 + 112) = 220 meters. The time taken to cross is given as 6 seconds. To find the speed of the second train, we need to convert the time from seconds to hours. 6 seconds is equal to 6/3600 hours. Speed is calculated by dividing the distance by time, so the speed of the second train is (220 / (6/3600)) = 220 * 3600 / 6 = 4400 km/hr. However, this is the combined speed of both trains. To find the speed of the second train alone, we subtract the speed of the first train (50 km/hr) from the combined speed, which gives us 4400 - 50 = 4350 km/hr. Converting this to km/hr, we get 4350 * 5/18 = 1450/3 = 483.33 m/s. Finally, converting this to km/hr, we get 483.33 * 3600 / 1000 = 1740 km/hr. Rounding off to the nearest whole number, we get the speed of the second train as 82 km/hr.

Explanation

When two trains are moving towards each other, the length of both trains is added to get the total distance that needs to be covered for the crossing. In this question, the total distance to be covered is (108 + 112) = 220 meters. The time taken to cross is given as 6 seconds. To find the speed of the second train, we need to convert the time from seconds to hours. 6 seconds is equal to 6/3600 hours. Speed is calculated by dividing the distance by time, so the speed of the second train is (220 / (6/3600)) = 220 * 3600 / 6 = 4400 km/hr. However, this is the combined speed of both trains. To find the speed of the second train alone, we subtract the speed of the first train (50 km/hr) from the combined speed, which gives us 4400 - 50 = 4350 km/hr. Converting this to km/hr, we get 4350 * 5/18 = 1450/3 = 483.33 m/s. Finally, converting this to km/hr, we get 483.33 * 3600 / 1000 = 1740 km/hr. Rounding off to the nearest whole number, we get the speed of the second train as 82 km/hr.

80. Sakshi invests a part of Rs. 12,000 in 12% stock at Rs. 120 and the remainder in 15% stock at Rs. 125. If his total dividend per annum is Rs. 1360, how much does he invest in 12% stock at Rs. 120?

Rs 4000

Rs 4500

Rs 5500

Rs 6000

Let x be the amount invested in the 12% stock at Rs. 120. The remainder, 12000 - x, is invested in the 15% stock at Rs. 125. The dividend from the 12% stock is 0.12x and the dividend from the 15% stock is 0.15(12000 - x). The total dividend per annum is the sum of these two dividends, so we have the equation 0.12x + 0.15(12000 - x) = 1360. Solving this equation, we find x = 4000. Therefore, Sakshi invests Rs. 4000 in the 12% stock at Rs. 120.

Explanation

Let x be the amount invested in the 12% stock at Rs. 120. The remainder, 12000 - x, is invested in the 15% stock at Rs. 125. The dividend from the 12% stock is 0.12x and the dividend from the 15% stock is 0.15(12000 - x). The total dividend per annum is the sum of these two dividends, so we have the equation 0.12x + 0.15(12000 - x) = 1360. Solving this equation, we find x = 4000. Therefore, Sakshi invests Rs. 4000 in the 12% stock at Rs. 120.

81. . Help yourself....................whatever you can use without wasting

With

To

In

For

The word "to" is used to indicate direction or purpose. In this context, it suggests that the action or result is being done or achieved for a specific purpose or goal.

Explanation

The word "to" is used to indicate direction or purpose. In this context, it suggests that the action or result is being done or achieved for a specific purpose or goal.

82. How many times are the hands of a clock at right angle in a day?

22

24

44

48

The hour hand of a clock moves 30 degrees in one hour, while the minute hand moves 6 degrees in one minute. To form a right angle, the hands of the clock must be 90 degrees apart. This occurs twice in every hour, as the minute hand moves around the clock face. Therefore, in a 24-hour day, the hands of a clock are at a right angle 44 times.

Explanation

The hour hand of a clock moves 30 degrees in one hour, while the minute hand moves 6 degrees in one minute. To form a right angle, the hands of the clock must be 90 degrees apart. This occurs twice in every hour, as the minute hand moves around the clock face. Therefore, in a 24-hour day, the hands of a clock are at a right angle 44 times.

83. How is the decimal value for 30 represented in binary?

00001111

00011010

00011110

00011111

The correct answer is 00011111. In binary, each digit represents a power of 2, starting from the rightmost digit. Adding up the corresponding powers of 2 for the 1's in the binary representation gives us the decimal value. In this case, 00011111 represents 16 + 8 + 4 + 2 + 1, which equals 31.

Explanation

The correct answer is 00011111. In binary, each digit represents a power of 2, starting from the rightmost digit. Adding up the corresponding powers of 2 for the 1's in the binary representation gives us the decimal value. In this case, 00011111 represents 16 + 8 + 4 + 2 + 1, which equals 31.

84. How many times in a day, the hands of a clock are straight?

22

24

44

48

The hour and minute hands of a clock are straight twice in an hour, once when they are aligned at 12 o'clock and once when they are aligned at 6 o'clock. In a day, there are 24 hours, so the hands of a clock are straight 24 times. However, we need to consider that the hands can also be straight at times like 1:05, 2:10, 3:15, etc., where the minute hand is at a multiple of 5. There are 12 such instances in an hour, so in a day, the hands of a clock are straight 24 + (12 x 24) = 24 + 288 = 312 times.

Explanation

The hour and minute hands of a clock are straight twice in an hour, once when they are aligned at 12 o'clock and once when they are aligned at 6 o'clock. In a day, there are 24 hours, so the hands of a clock are straight 24 times. However, we need to consider that the hands can also be straight at times like 1:05, 2:10, 3:15, etc., where the minute hand is at a multiple of 5. There are 12 such instances in an hour, so in a day, the hands of a clock are straight 24 + (12 x 24) = 24 + 288 = 312 times.

85. . The output of the code below is #include int x; void main() { if (X) printf("hi"); else printf("how are u"); }

Hi

How are your

Compile time error

None of the mentioned

The reason the output of the code is "how are u" is because the variable "x" is not defined or initialized before the if statement. Therefore, the condition "if (x)" will evaluate to false, and the code will execute the else statement, which prints "how are u".

Explanation

The reason the output of the code is "how are u" is because the variable "x" is not defined or initialized before the if statement. Therefore, the condition "if (x)" will evaluate to false, and the code will execute the else statement, which prints "how are u".