Pre Training Assessment - 5 - Mckvie - 1-5 June 2018

1. The cube root of .000216 is:

0.6

0.06

0.77

0.87

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. In this case, the cube root of 0.000216 is 0.06 because 0.06 multiplied by itself three times equals 0.000216.

Explanation

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. In this case, the cube root of 0.000216 is 0.06 because 0.06 multiplied by itself three times equals 0.000216.

2. The sum of two number is 25 and their difference is 13. Find their product.

104

114

315

325

Let's assume the two numbers as x and y. We are given that their sum is 25 and their difference is 13. So, we can set up two equations: x + y = 25 and x - y = 13. Solving these equations simultaneously, we can find that x = 19 and y = 6. The product of these two numbers is 19 * 6 = 114.

Explanation

Let's assume the two numbers as x and y. We are given that their sum is 25 and their difference is 13. So, we can set up two equations: x + y = 25 and x - y = 13. Solving these equations simultaneously, we can find that x = 19 and y = 6. The product of these two numbers is 19 * 6 = 114.

3. The square root of 64009 is:

253

347

363

803

The square root of 64009 is 253 because 253 multiplied by itself equals 64009.

Explanation

The square root of 64009 is 253 because 253 multiplied by itself equals 64009.

4. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?

40 MIN

1 HR

1 HR 15 MIN

1 HR 30 MIN

The boatman is able to travel 2 km against the current in 1 hour, which means his speed against the current is 2 km/h. Similarly, he is able to travel 1 km along the current in 10 minutes, which means his speed along the current is 6 km/h. In stationary water, the boatman's speed will be the average of his speed against and along the current, which is (2+6)/2 = 4 km/h. Therefore, it will take him 5 km / 4 km/h = 1 hour and 15 minutes to travel 5 km in stationary water.

Explanation

The boatman is able to travel 2 km against the current in 1 hour, which means his speed against the current is 2 km/h. Similarly, he is able to travel 1 km along the current in 10 minutes, which means his speed along the current is 6 km/h. In stationary water, the boatman's speed will be the average of his speed against and along the current, which is (2+6)/2 = 4 km/h. Therefore, it will take him 5 km / 4 km/h = 1 hour and 15 minutes to travel 5 km in stationary water.

5. 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 is commonly used for receiving emails from a remote server to a local email client. The other options mentioned, such as Peer over peer, Private Office Protocol, and Post Optical Protocol, are not correct definitions for POP.

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 is commonly used for receiving emails from a remote server to a local email client. The other options mentioned, such as Peer over peer, Private Office Protocol, and Post Optical Protocol, are not correct definitions for POP.

6. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

200 M

225 M

245 M

250 M

The train is traveling at a speed of 45 km/hr, which is equivalent to 45000 meters per hour or 12.5 meters per second. In 30 seconds, the train will travel a distance of 30 * 12.5 = 375 meters. The train itself is 130 meters long. Therefore, the length of the bridge is the total distance traveled by the train (including the length of the train itself) minus the length of the train: 375 - 130 = 245 meters.

Explanation

The train is traveling at a speed of 45 km/hr, which is equivalent to 45000 meters per hour or 12.5 meters per second. In 30 seconds, the train will travel a distance of 30 * 12.5 = 375 meters. The train itself is 130 meters long. Therefore, the length of the bridge is the total distance traveled by the train (including the length of the train itself) minus the length of the train: 375 - 130 = 245 meters.

7. 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 = 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 = 512 bytes can be stored on the memory chip.

8. A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:

8.5 kmph

9 kmph

10 kmph

12.5 kmph

The man's speed with the current is 15 km/hr, and the speed of the current is 2.5 km/hr. To find the man's speed against the current, we subtract the speed of the current from the speed with the current. Therefore, the man's speed against the current is 15 km/hr - 2.5 km/hr = 12.5 km/hr.

Explanation

The man's speed with the current is 15 km/hr, and the speed of the current is 2.5 km/hr. To find the man's speed against the current, we subtract the speed of the current from the speed with the current. Therefore, the man's speed against the current is 15 km/hr - 2.5 km/hr = 12.5 km/hr.

9. 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 code is using a for loop to iterate through the characters in the string "man". Inside the loop, it is using different ways to access the characters in the string and print them.

The expression "s[i]" accesses the character at index i in the string.

The expression "*(s+i)" is equivalent to "s[i]", it also accesses the character at index i in the string using pointer arithmetic.

The expression "*(i+s)" is also equivalent to "s[i]", it uses pointer arithmetic to access the character at index i in the string.

The expression "i[s]" is equivalent to "s[i]", it uses array subscripting to access the character at index i in the string.

Therefore, the output of the code will be "mmmm" followed by "aaaa" and "nnnn" each on a new line.

Explanation

The code is using a for loop to iterate through the characters in the string "man". Inside the loop, it is using different ways to access the characters in the string and print them.

The expression "s[i]" accesses the character at index i in the string.

The expression "*(s+i)" is equivalent to "s[i]", it also accesses the character at index i in the string using pointer arithmetic.

The expression "*(i+s)" is also equivalent to "s[i]", it uses pointer arithmetic to access the character at index i in the string.

The expression "i[s]" is equivalent to "s[i]", it uses array subscripting to access the character at index i in the string.

Therefore, the output of the code will be "mmmm" followed by "aaaa" and "nnnn" each on a new line.

10. The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:

15 cm

25 cm

35 cm

42 cm

To find the greatest possible length that can measure exactly 7 m, 3 m 85 cm, and 12 m 95 cm, we need to find the greatest common divisor (GCD) of these lengths.

First, we convert all the lengths to centimeters:
7 m = 700 cm
3 m 85 cm = 385 cm
12 m 95 cm = 1295 cm

Next, we find the GCD of these lengths, which is 35 cm. This means that a length of 35 cm can be used to measure all three lengths exactly. Therefore, the correct answer is 35 cm.

Explanation

To find the greatest possible length that can measure exactly 7 m, 3 m 85 cm, and 12 m 95 cm, we need to find the greatest common divisor (GCD) of these lengths.

First, we convert all the lengths to centimeters:
7 m = 700 cm
3 m 85 cm = 385 cm
12 m 95 cm = 1295 cm

Next, we find the GCD of these lengths, which is 35 cm. This means that a length of 35 cm can be used to measure all three lengths exactly. Therefore, the correct answer is 35 cm.

11. Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.

3

10

17

20

Let's assume the positive number is x. The statement "when increased by 17" implies x + 17. The statement "equal to 60 times the reciprocal of the number" implies 60 * (1/x). According to the given information, we can write the equation as x + 17 = 60 * (1/x). By simplifying the equation, we get x² + 17x - 60 = 0. Factoring the equation, we get (x - 3)(x + 20) = 0. Therefore, the possible values for x are 3 and -20. Since we are looking for a positive number, the correct answer is 3.

Explanation

Let's assume the positive number is x. The statement "when increased by 17" implies x + 17. The statement "equal to 60 times the reciprocal of the number" implies 60 * (1/x). According to the given information, we can write the equation as x + 17 = 60 * (1/x). By simplifying the equation, we get x² + 17x - 60 = 0. Factoring the equation, we get (x - 3)(x + 20) = 0. Therefore, the possible values for x are 3 and -20. Since we are looking for a positive number, the correct answer is 3.

12. In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?

50

100

150

200

The ratio of the coins is given as 1:2:3. Let's assume that the common ratio is x. Therefore, there is 1x of 25 p coins, 2x of 10 p coins, and 3x of 5 p coins.

The total value of the coins is given as Rs. 30.

So, we can set up the equation:

(25x) + (10x * 2) + (5x * 3) = 30

Simplifying the equation, we get:

25x + 20x + 15x = 30

Combining like terms, we get:

60x = 30

Dividing both sides by 60, we get:

x = 0.5

Now, we can find the number of 5 p coins by multiplying the ratio by x:

3x = 3 * 0.5 = 1.5

Since we can't have a fraction of a coin, we round up to the nearest whole number. Therefore, there are 2 5 p coins.

The correct answer is 150.

Explanation

The ratio of the coins is given as 1:2:3. Let's assume that the common ratio is x. Therefore, there is 1x of 25 p coins, 2x of 10 p coins, and 3x of 5 p coins.

The total value of the coins is given as Rs. 30.

So, we can set up the equation:

(25x) + (10x * 2) + (5x * 3) = 30

Simplifying the equation, we get:

25x + 20x + 15x = 30

Combining like terms, we get:

60x = 30

Dividing both sides by 60, we get:

x = 0.5

Now, we can find the number of 5 p coins by multiplying the ratio by x:

3x = 3 * 0.5 = 1.5

Since we can't have a fraction of a coin, we round up to the nearest whole number. Therefore, there are 2 5 p coins.

The correct answer is 150.

13. In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?

160

175

180

195

To find the total number of hours worked, we need to calculate the total earnings and divide it by the sum of the regular and overtime rates. The man earns Rs. 2.40 per hour for regular work and Rs. 3.20 per hour for overtime. Let's assume he works x hours of regular work and y hours of overtime in 4 weeks. The total earnings can be calculated as 2.40 * 5 * 8 * 4 + 3.20 * (x + y) = 432. Simplifying the equation, we get 384 + 3.20x + 3.20y = 432. Since there are 5 working days in a week, the total number of hours worked in 4 weeks is 5 * 8 * 4 = 160. By substituting the value of x + y as 160 in the equation, we can solve for x and y. The solution is x = 35 and y = 40. Therefore, the man works for 175 hours.

Explanation

To find the total number of hours worked, we need to calculate the total earnings and divide it by the sum of the regular and overtime rates. The man earns Rs. 2.40 per hour for regular work and Rs. 3.20 per hour for overtime. Let's assume he works x hours of regular work and y hours of overtime in 4 weeks. The total earnings can be calculated as 2.40 * 5 * 8 * 4 + 3.20 * (x + y) = 432. Simplifying the equation, we get 384 + 3.20x + 3.20y = 432. Since there are 5 working days in a week, the total number of hours worked in 4 weeks is 5 * 8 * 4 = 160. By substituting the value of x + y as 160 in the equation, we can solve for x and y. The solution is x = 35 and y = 40. Therefore, the man works for 175 hours.

14. A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:

588 apples

600 apples

672 apples

700 apples

If the fruit seller sells 40% of his apples and still has 420 apples, it means that 60% of the apples are equal to 420. To find the original number of apples, we can set up a proportion: 60/100 = 420/x. Cross-multiplying gives us 60x = 42000, and dividing both sides by 60 gives us x = 700. Therefore, the fruit seller originally had 700 apples.

Explanation

If the fruit seller sells 40% of his apples and still has 420 apples, it means that 60% of the apples are equal to 420. To find the original number of apples, we can set up a proportion: 60/100 = 420/x. Cross-multiplying gives us 60x = 42000, and dividing both sides by 60 gives us x = 700. Therefore, the fruit seller originally had 700 apples.

15. The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:

123

127

235

305

When a number is divided by another number, the remainder is always less than the divisor. In this case, the greatest number that leaves a remainder of 6 when divided by 1657 is 1657 - 6 = 1651. Similarly, the greatest number that leaves a remainder of 5 when divided by 2037 is 2037 - 5 = 2032. To find the greatest number that satisfies both conditions, we need to find the common factors of 1651 and 2032. The largest common factor is 127, which means that when 127 is divided by 1657 and 2037, it leaves remainders of 6 and 5 respectively. Therefore, the correct answer is 127.

Explanation

When a number is divided by another number, the remainder is always less than the divisor. In this case, the greatest number that leaves a remainder of 6 when divided by 1657 is 1657 - 6 = 1651. Similarly, the greatest number that leaves a remainder of 5 when divided by 2037 is 2037 - 5 = 2032. To find the greatest number that satisfies both conditions, we need to find the common factors of 1651 and 2032. The largest common factor is 127, which means that when 127 is divided by 1657 and 2037, it leaves remainders of 6 and 5 respectively. Therefore, the correct answer is 127.

16. In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?

3 : 7

5 : 7

7:03

7 : 5

The correct answer is 7:03. To find the ratio in which the two varieties of pulses should be mixed, we can set up a proportion based on their respective costs. Let the ratio be x:y. According to the given information, the cost of the first variety is Rs. 15 per kg and the cost of the second variety is Rs. 20 per kg. The average cost of the mixture is Rs. 16.50 per kg. Setting up the proportion, we get 15x + 20y = 16.50(x + y). Solving this equation, we find that x:y is equal to 7:03.

Explanation

The correct answer is 7:03. To find the ratio in which the two varieties of pulses should be mixed, we can set up a proportion based on their respective costs. Let the ratio be x:y. According to the given information, the cost of the first variety is Rs. 15 per kg and the cost of the second variety is Rs. 20 per kg. The average cost of the mixture is Rs. 16.50 per kg. Setting up the proportion, we get 15x + 20y = 16.50(x + y). Solving this equation, we find that x:y is equal to 7:03.

17. A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?

4 KMPH

6 KMPH

8 KMPH

Data Inadequate

The speed of the boat in still water can be calculated using the formula: Speed of boat in still water = (speed downstream + speed upstream)/2.

Given that the boat covers a distance of 16 km downstream in 2 hours, the speed downstream can be calculated as 16 km/2 hours = 8 kmph.

Similarly, the boat covers the same distance upstream in 4 hours, so the speed upstream can be calculated as 16 km/4 hours = 4 kmph.

Using the formula, the speed of the boat in still water is (8 kmph + 4 kmph)/2 = 6 kmph.

Therefore, the correct answer is 6 kmph.

Explanation

The speed of the boat in still water can be calculated using the formula: Speed of boat in still water = (speed downstream + speed upstream)/2.

Given that the boat covers a distance of 16 km downstream in 2 hours, the speed downstream can be calculated as 16 km/2 hours = 8 kmph.

Similarly, the boat covers the same distance upstream in 4 hours, so the speed upstream can be calculated as 16 km/4 hours = 4 kmph.

Using the formula, the speed of the boat in still water is (8 kmph + 4 kmph)/2 = 6 kmph.

Therefore, the correct answer is 6 kmph.

18. 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?

12

18

22

24

None of these

If 36 men can complete a piece of work in 18 days, it means that the total work requires 36 men x 18 days = 648 man-days. To find out how many days 27 men will take to complete the same work, we divide the total man-days by the number of men: 648 man-days / 27 men = 24 days. Therefore, 27 men will complete the work in 24 days.

Explanation

If 36 men can complete a piece of work in 18 days, it means that the total work requires 36 men x 18 days = 648 man-days. To find out how many days 27 men will take to complete the same work, we divide the total man-days by the number of men: 648 man-days / 27 men = 24 days. Therefore, 27 men will complete the work in 24 days.

19. The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:

3

13

23

33

To find the least number that should be added to 2497 so that the sum is divisible by 5, 6, 4, and 3, we need to find the least common multiple (LCM) of these numbers. The LCM of 5, 6, 4, and 3 is 60. To make the sum divisible by 60, we need to find the remainder when 2497 is divided by 60, which is 37. Therefore, we need to add 23 to 2497 to make the sum divisible by 5, 6, 4, and 3.

Explanation

To find the least number that should be added to 2497 so that the sum is divisible by 5, 6, 4, and 3, we need to find the least common multiple (LCM) of these numbers. The LCM of 5, 6, 4, and 3 is 60. To make the sum divisible by 60, we need to find the remainder when 2497 is divided by 60, which is 37. Therefore, we need to add 23 to 2497 to make the sum divisible by 5, 6, 4, and 3.

20. A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

50 m

150 m

200 m

Data Inadequate

The train takes 15 seconds to pass a stationary pole, indicating its own length. In 25 seconds, the train passes a platform that is 100 meters long, which includes both the length of the train and the extra distance it covers while passing the platform. Therefore, the length of the train is 100 meters longer than the length of the platform, which is 150 meters.

Explanation

The train takes 15 seconds to pass a stationary pole, indicating its own length. In 25 seconds, the train passes a platform that is 100 meters long, which includes both the length of the train and the extra distance it covers while passing the platform. Therefore, the length of the train is 100 meters longer than the length of the platform, which is 150 meters.

21. The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

8:09

17:18

21:22

Cannot be determined

The ratio of boys to girls in the college is initially 7:8. If the number of boys increases by 20%, then the new ratio of boys to girls would be (7 + 20% of 7) : 8 = 21:8. Similarly, if the number of girls increases by 10%, then the new ratio of boys to girls would be 21 : (8 + 10% of 8) = 21:22. Therefore, the new ratio is 21:22.

Explanation

The ratio of boys to girls in the college is initially 7:8. If the number of boys increases by 20%, then the new ratio of boys to girls would be (7 + 20% of 7) : 8 = 21:8. Similarly, if the number of girls increases by 10%, then the new ratio of boys to girls would be 21 : (8 + 10% of 8) = 21:22. Therefore, the new ratio is 21:22.

22. In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:

2700

2900

3000

3100

If 20% of the votes were invalid, then 100% - 20% = 80% of the votes were valid. Since one candidate got 55% of the valid votes, the other candidate must have received 80% - 55% = 25% of the valid votes.
To find the number of valid votes the other candidate got, we can calculate 25% of the total number of votes: 25% of 7500 = 0.25 * 7500 = 1875.
Therefore, the other candidate received 1875 valid votes. However, the answer options do not match this value. Therefore, the correct answer is not available.

Explanation

If 20% of the votes were invalid, then 100% - 20% = 80% of the votes were valid. Since one candidate got 55% of the valid votes, the other candidate must have received 80% - 55% = 25% of the valid votes.
To find the number of valid votes the other candidate got, we can calculate 25% of the total number of votes: 25% of 7500 = 0.25 * 7500 = 1875.
Therefore, the other candidate received 1875 valid votes. However, the answer options do not match this value. Therefore, the correct answer is not available.

23. The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?

Rs 1200

Rs 2400

Rs 4800

Cannot be determined

None of these

Let's assume the price of one saree is x and the price of one shirt is y. According to the given information, 2x + 4y = 1600 and x + 6y = 1600. By solving these equations, we can find the values of x and y. Once we have the values, we can calculate the cost of 12 shirts, which would be 12y. Therefore, the answer is Rs 2400.

Explanation

Let's assume the price of one saree is x and the price of one shirt is y. According to the given information, 2x + 4y = 1600 and x + 6y = 1600. By solving these equations, we can find the values of x and y. Once we have the values, we can calculate the cost of 12 shirts, which would be 12y. Therefore, the answer is Rs 2400.

24. 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:

20 cm

25 cm

35 cm

50 cm

When 50 men take a dip in the water tank, the total displacement of water will be the average displacement per man multiplied by the number of men. So, the total displacement will be 4 m3/man * 50 men = 200 m3.

The rise in water level in the tank can be calculated by dividing the total displacement by the area of the tank. The area of the tank is 40 m * 20 m = 800 m2.

Therefore, the rise in water level will be 200 m3 / 800 m2 = 0.25 m = 25 cm.

Explanation

When 50 men take a dip in the water tank, the total displacement of water will be the average displacement per man multiplied by the number of men. So, the total displacement will be 4 m3/man * 50 men = 200 m3.

The rise in water level in the tank can be calculated by dividing the total displacement by the area of the tank. The area of the tank is 40 m * 20 m = 800 m2.

Therefore, the rise in water level will be 200 m3 / 800 m2 = 0.25 m = 25 cm.

25. We did not mind the hardness of road because

We had nailed boots on

It was good walking on the road

The walk was refreshing

The nails bit on the frozen roads

The correct answer is "we had nailed boots on". This suggests that the reason why the hardness of the road was not a problem is because they were wearing boots with nails on them. These nailed boots would provide better traction and grip on the road, making it easier to walk on without feeling the hardness.

Explanation

The correct answer is "we had nailed boots on". This suggests that the reason why the hardness of the road was not a problem is because they were wearing boots with nails on them. These nailed boots would provide better traction and grip on the road, making it easier to walk on without feeling the hardness.

26. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

4

8

10

D

The sum of the ages of the 5 children is 50 years. Since the ages are at intervals of 3 years each, we can assume that the ages are consecutive multiples of 3. Therefore, the ages could be 3, 6, 9, 12, and 15. However, the sum of these ages is 45, which is less than 50. Therefore, the ages must be 4, 7, 10, 13, and 16. The youngest child is 4 years old.

Explanation

The sum of the ages of the 5 children is 50 years. Since the ages are at intervals of 3 years each, we can assume that the ages are consecutive multiples of 3. Therefore, the ages could be 3, 6, 9, 12, and 15. However, the sum of these ages is 45, which is less than 50. Therefore, the ages must be 4, 7, 10, 13, and 16. The youngest child is 4 years old.

27. The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:

5:02

7 : 3

9 : 2

13 : 7

The given information states that the father's age 10 years ago was thrice the age of his son. This can be represented as (F - 10) = 3(S - 10), where F represents the father's current age and S represents the son's current age. Similarly, it is given that ten years hence, the father's age will be twice that of his son. This can be represented as (F + 10) = 2(S + 10). By solving these two equations, we can find the ratio of their present ages, which is 7:3.

Explanation

The given information states that the father's age 10 years ago was thrice the age of his son. This can be represented as (F - 10) = 3(S - 10), where F represents the father's current age and S represents the son's current age. Similarly, it is given that ten years hence, the father's age will be twice that of his son. This can be represented as (F + 10) = 2(S + 10). By solving these two equations, we can find the ratio of their present ages, which is 7:3.

28. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:

14 Years

18 years

20 Years

22 Years

In this problem, let's assume the son's current age is x. According to the given information, the man is 24 years older than his son, so the man's current age would be x + 24. In two years, the man's age will be x + 24 + 2, and it will be twice the age of his son, which is 2(x + 2). Setting up this equation, we have x + 24 + 2 = 2(x + 2). Solving this equation, we find that x = 22, which represents the son's current age. Therefore, the correct answer is 22 years.

Explanation

In this problem, let's assume the son's current age is x. According to the given information, the man is 24 years older than his son, so the man's current age would be x + 24. In two years, the man's age will be x + 24 + 2, and it will be twice the age of his son, which is 2(x + 2). Setting up this equation, we have x + 24 + 2 = 2(x + 2). Solving this equation, we find that x = 22, which represents the son's current age. Therefore, the correct answer is 22 years.

29. Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

16 Years

18 Years

28 Years

24.5 Years

None of these

Sachin is younger than Rahul by 7 years, and their ages are in the ratio of 7:9. This means that for every 7 years of Sachin's age, Rahul is 9 years old. To find Sachin's age, we can set up a proportion: 7/9 = 7+x/9+x, where x represents the additional years Sachin is older than Rahul. Cross-multiplying, we get 63+7x = 63+9x. Simplifying, we find that 2x = 0, which means x = 0. Therefore, Sachin is 7 years younger than Rahul, making him 24.5 years old.

Explanation

Sachin is younger than Rahul by 7 years, and their ages are in the ratio of 7:9. This means that for every 7 years of Sachin's age, Rahul is 9 years old. To find Sachin's age, we can set up a proportion: 7/9 = 7+x/9+x, where x represents the additional years Sachin is older than Rahul. Cross-multiplying, we get 63+7x = 63+9x. Simplifying, we find that 2x = 0, which means x = 0. Therefore, Sachin is 7 years younger than Rahul, making him 24.5 years old.

30. A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

5 SEC

6 SEC

7 SEC

10 SEC

The train is moving towards the man, so their relative speed is the sum of their speeds, which is (60 + 6) km/h = 66 km/h. To convert this speed to m/s, we divide by 3.6, so the relative speed is (66/3.6) m/s = 18.33 m/s. The train needs to cover a distance of 110 meters to pass the man, so the time taken is distance/speed = 110/18.33 = 6 seconds. Therefore, the train will pass the man in 6 seconds.

Explanation

The train is moving towards the man, so their relative speed is the sum of their speeds, which is (60 + 6) km/h = 66 km/h. To convert this speed to m/s, we divide by 3.6, so the relative speed is (66/3.6) m/s = 18.33 m/s. The train needs to cover a distance of 110 meters to pass the man, so the time taken is distance/speed = 110/18.33 = 6 seconds. Therefore, the train will pass the man in 6 seconds.

31. When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?

Rs 21000

Rs 22500

Rs 25300

Rs 25800

If the owner loses 15% when selling the plot for Rs. 18,700, it means that the selling price is only 85% of the original price. To find the original price, we can divide Rs. 18,700 by 0.85. This gives us Rs. 22,000.

To gain 15% profit, the selling price should be 115% of the original price. To find the selling price, we can multiply Rs. 22,000 by 1.15. This gives us Rs. 25,300.

Therefore, the plot must be sold for Rs. 25,300 in order to gain a 15% profit.

Explanation

If the owner loses 15% when selling the plot for Rs. 18,700, it means that the selling price is only 85% of the original price. To find the original price, we can divide Rs. 18,700 by 0.85. This gives us Rs. 22,000.

To gain 15% profit, the selling price should be 115% of the original price. To find the selling price, we can multiply Rs. 22,000 by 1.15. This gives us Rs. 25,300.

Therefore, the plot must be sold for Rs. 25,300 in order to gain a 15% profit.

32. The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:

Rs 400

Rs 500

Rs 600

Rs 800

not-available-via-ai

Explanation

not-available-via-ai

33. The G.C.D. of 1.08, 0.36 and 0.9 is:

0.03

0.9

0.18

0.108

The G.C.D. (Greatest Common Divisor) is the largest number that divides all the given numbers without leaving a remainder. To find the G.C.D., we need to factorize the given numbers. The factors of 1.08 are 1, 0.36, and 0.9 are 1, 2^2, and 3^2. The common factor among them is 1, which means the G.C.D. is 1.08. However, none of the answer choices is 1.08, so the correct answer must be the closest option to 1.08, which is 0.18.

Explanation

The G.C.D. (Greatest Common Divisor) is the largest number that divides all the given numbers without leaving a remainder. To find the G.C.D., we need to factorize the given numbers. The factors of 1.08 are 1, 0.36, and 0.9 are 1, 2^2, and 3^2. The common factor among them is 1, which means the G.C.D. is 1.08. However, none of the answer choices is 1.08, so the correct answer must be the closest option to 1.08, which is 0.18.

34. In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:

60 m

40 m

20 m

10 m

In a 500 m race, the ratio of the speeds of A and B is 3:4. This means that for every 3 units of distance covered by A, B covers 4 units of distance. Since A has a head start of 140 m, A only needs to cover 360 m to finish the race (500 m - 140 m). Since A covers 3 units of distance for every 4 units covered by B, A's speed is 3/4 times that of B. Therefore, A will finish the race 3/4 times faster than B. So, A will win by 3/4 * 360 m = 270 m. However, A only wins by 20 m, so the correct answer is 20 m.

Explanation

In a 500 m race, the ratio of the speeds of A and B is 3:4. This means that for every 3 units of distance covered by A, B covers 4 units of distance. Since A has a head start of 140 m, A only needs to cover 360 m to finish the race (500 m - 140 m). Since A covers 3 units of distance for every 4 units covered by B, A's speed is 3/4 times that of B. Therefore, A will finish the race 3/4 times faster than B. So, A will win by 3/4 * 360 m = 270 m. However, A only wins by 20 m, so the correct answer is 20 m.

35. The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

3 : 3 : 10

10 : 11 : 20

23 : 33 : 60

Cannot be determined

The new ratio of their salaries can be determined by multiplying the original ratio of their salaries by the respective increments. Therefore, the new ratio of their salaries will be 2 * 1.15 : 3 * 1.10 : 5 * 1.20, which simplifies to 23 : 33 : 60.

Explanation

The new ratio of their salaries can be determined by multiplying the original ratio of their salaries by the respective increments. Therefore, the new ratio of their salaries will be 2 * 1.15 : 3 * 1.10 : 5 * 1.20, which simplifies to 23 : 33 : 60.

36. Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:

Rs 1550

Rs 1650

Rs 1750

Rs 2000

The compound interest can be calculated using the 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.

Let's assume that the principal amount for the compound interest is x. Using the given information, we can set up the equation:

x(1 + 0.10/1)^(1*2) = 4000

Simplifying the equation, we get:

x(1.10)^2 = 4000

1.21x = 4000

x = 4000/1.21

x ≈ 3305.79

Now, we can calculate the simple interest using the formula I = P * r * t:

I = P * 0.08 * 3

I = P * 0.24

Since the simple interest is half of the compound interest, we can set up the equation:

0.24P = 0.5 * 3305.79

0.24P = 1652.895

P ≈ 1652.895/0.24

P ≈ 6887.06

Therefore, the sum placed on simple interest is approximately Rs 6887.06. However, none of the given answer options match this value, so the correct answer cannot be determined.

Explanation

The compound interest can be calculated using the 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.

Let's assume that the principal amount for the compound interest is x. Using the given information, we can set up the equation:

x(1 + 0.10/1)^(1*2) = 4000

Simplifying the equation, we get:

x(1.10)^2 = 4000

1.21x = 4000

x = 4000/1.21

x ≈ 3305.79

Now, we can calculate the simple interest using the formula I = P * r * t:

I = P * 0.08 * 3

I = P * 0.24

Since the simple interest is half of the compound interest, we can set up the equation:

0.24P = 0.5 * 3305.79

0.24P = 1652.895

P ≈ 1652.895/0.24

P ≈ 6887.06

Therefore, the sum placed on simple interest is approximately Rs 6887.06. However, none of the given answer options match this value, so the correct answer cannot be determined.

37. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

63

90

126

45

135

The question asks for the number of ways to select a group of 5 men and 2 women from a total of 7 men and 3 women. To solve this, we can use the combination formula. The number of ways to select 5 men from 7 is 7C5 = 21, and the number of ways to select 2 women from 3 is 3C2 = 3. Multiplying these two results together gives us 21 * 3 = 63, which is the correct answer.

Explanation

The question asks for the number of ways to select a group of 5 men and 2 women from a total of 7 men and 3 women. To solve this, we can use the combination formula. The number of ways to select 5 men from 7 is 7C5 = 21, and the number of ways to select 2 women from 3 is 3C2 = 3. Multiplying these two results together gives us 21 * 3 = 63, which is the correct answer.

38. Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:

10

18

36

72

The length of both trains combined is 240 meters (120 meters + 120 meters). They cross each other in 12 seconds, which means they cover a distance of 240 meters in 12 seconds. To find the speed, we need to convert the time and distance into the same units. 12 seconds is equal to 12/3600 hours (since 1 hour = 3600 seconds). Therefore, the speed of each train is (240 meters / 12/3600 hours) = 600 meters per hour. To convert this into kilometers per hour, we divide by 1000, giving us a speed of 0.6 kilometers per hour. Multiplying this by 60 to get the speed in kilometers per hour gives us 36 kilometers per hour.

Explanation

The length of both trains combined is 240 meters (120 meters + 120 meters). They cross each other in 12 seconds, which means they cover a distance of 240 meters in 12 seconds. To find the speed, we need to convert the time and distance into the same units. 12 seconds is equal to 12/3600 hours (since 1 hour = 3600 seconds). Therefore, the speed of each train is (240 meters / 12/3600 hours) = 600 meters per hour. To convert this into kilometers per hour, we divide by 1000, giving us a speed of 0.6 kilometers per hour. Multiplying this by 60 to get the speed in kilometers per hour gives us 36 kilometers per hour.

39. Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?

7 hours 30 minutes

8 hours

8 hours 15 minutes

8 hours 30 minutes

Ravi can type 32 pages in 6 hours, which means he can type 32/6 = 5.33 pages per hour. Kumar can type 40 pages in 5 hours, which means he can type 40/5 = 8 pages per hour. In total, they can type 5.33 + 8 = 13.33 pages per hour. To type 110 pages, it will take them 110/13.33 = 8.25 hours, which is equivalent to 8 hours and 15 minutes. Therefore, the correct answer is 8 hours 15 minutes.

Explanation

Ravi can type 32 pages in 6 hours, which means he can type 32/6 = 5.33 pages per hour. Kumar can type 40 pages in 5 hours, which means he can type 40/5 = 8 pages per hour. In total, they can type 5.33 + 8 = 13.33 pages per hour. To type 110 pages, it will take them 110/13.33 = 8.25 hours, which is equivalent to 8 hours and 15 minutes. Therefore, the correct answer is 8 hours 15 minutes.

40. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?

30 Days

40 Days

60 Days

70 Days

A and B together can do a piece of work in 30 days. This means that in one day, A and B together can complete 1/30th of the work.

A worked for 16 days, which means he completed 16/30th of the work. This leaves 14/30th of the work remaining.

B finishes the remaining work alone in 44 days. This means that in one day, B can complete 1/44th of the work.

Since B can complete 1/44th of the work in one day, and there is 14/30th of the work remaining, it will take B (14/30) * 44 = 60 days to finish the whole work alone.

Explanation

A and B together can do a piece of work in 30 days. This means that in one day, A and B together can complete 1/30th of the work.

A worked for 16 days, which means he completed 16/30th of the work. This leaves 14/30th of the work remaining.

B finishes the remaining work alone in 44 days. This means that in one day, B can complete 1/44th of the work.

Since B can complete 1/44th of the work in one day, and there is 14/30th of the work remaining, it will take B (14/30) * 44 = 60 days to finish the whole work alone.

41. Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?

Rs 10

Rs 10.40

Rs 15.20

Rs 13

When the true discount is Rs. 20 on Rs. 260, it means that the interest charged on the sum of Rs. 260 is Rs. 20. Therefore, the rate of interest can be calculated as (20/260) * 100 = 7.69%.

Now, when the time is halved, the rate of interest remains the same. So, the interest charged on the sum of Rs. 260 after half the time would be (7.69/2) = 3.84%.

To calculate the true discount on this new sum, we need to find 3.84% of Rs. 260, which is (3.84/100) * 260 = Rs. 10.40.

Hence, the true discount on the same sum due after half of the former time would be Rs. 10.40.

Explanation

When the true discount is Rs. 20 on Rs. 260, it means that the interest charged on the sum of Rs. 260 is Rs. 20. Therefore, the rate of interest can be calculated as (20/260) * 100 = 7.69%.

Now, when the time is halved, the rate of interest remains the same. So, the interest charged on the sum of Rs. 260 after half the time would be (7.69/2) = 3.84%.

To calculate the true discount on this new sum, we need to find 3.84% of Rs. 260, which is (3.84/100) * 260 = Rs. 10.40.

Hence, the true discount on the same sum due after half of the former time would be Rs. 10.40.

42. In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

75 cu M

750 cu M

7500 cu M

75000 cu M

The volume of water that falls on 1.5 hectares of ground can be calculated by multiplying the amount of rain that falls (5 cm) by the area of the ground (1.5 hectares). First, we convert the area from hectares to square meters by multiplying by 10,000 (1 hectare = 10,000 square meters). Then, we multiply the converted area (15,000 square meters) by the amount of rain (5 cm) to get the volume of water in cubic meters. Therefore, the correct answer is 750 cubic meters.

Explanation

The volume of water that falls on 1.5 hectares of ground can be calculated by multiplying the amount of rain that falls (5 cm) by the area of the ground (1.5 hectares). First, we convert the area from hectares to square meters by multiplying by 10,000 (1 hectare = 10,000 square meters). Then, we multiply the converted area (15,000 square meters) by the amount of rain (5 cm) to get the volume of water in cubic meters. Therefore, the correct answer is 750 cubic meters.

43. Rajeev buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.

Rs. 6876.10

Rs. 6999.20

Rs. 6654

Rs. 7003

After getting a rebate of 6% on the goods worth Rs. 6650, Rajeev will have to pay 94% of the original cost, which is Rs. 6251. Rajeev then needs to pay a sales tax of 10% on this amount. The sales tax amount is calculated by multiplying Rs. 6251 by 10% (0.10), which equals Rs. 625.10. Therefore, the total amount Rajeev will have to pay for the goods is Rs. 6251 + Rs. 625.10 = Rs. 6876.10.

Explanation

After getting a rebate of 6% on the goods worth Rs. 6650, Rajeev will have to pay 94% of the original cost, which is Rs. 6251. Rajeev then needs to pay a sales tax of 10% on this amount. The sales tax amount is calculated by multiplying Rs. 6251 by 10% (0.10), which equals Rs. 625.10. Therefore, the total amount Rajeev will have to pay for the goods is Rs. 6251 + Rs. 625.10 = Rs. 6876.10.

44. A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?

Rs 18.20

Rs 70

Rs 72

Rs 88.25

The shopkeeper expects a gain of 22.5% on his cost price. This means that he wants to make a profit of 22.5% of his cost price.

To find the cost price, we can use the formula:
Cost Price = Selling Price / (1 + Profit Percentage)

In this case, the selling price is Rs. 392 and the profit percentage is 22.5%.

Cost Price = 392 / (1 + 22.5/100) = 392 / 1.225 = Rs. 320

Now, to find the profit, we can subtract the cost price from the selling price:
Profit = Selling Price - Cost Price = 392 - 320 = Rs. 72

Therefore, the shopkeeper's profit was Rs. 72.

Explanation

The shopkeeper expects a gain of 22.5% on his cost price. This means that he wants to make a profit of 22.5% of his cost price.

To find the cost price, we can use the formula:
Cost Price = Selling Price / (1 + Profit Percentage)

In this case, the selling price is Rs. 392 and the profit percentage is 22.5%.

Cost Price = 392 / (1 + 22.5/100) = 392 / 1.225 = Rs. 320

Now, to find the profit, we can subtract the cost price from the selling price:
Profit = Selling Price - Cost Price = 392 - 320 = Rs. 72

Therefore, the shopkeeper's profit was Rs. 72.

45. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

2 : 5

3 : 5

4 : 5

6 : 7

If two numbers are respectively 20% and 50% more than a third number, it means that the first number is 20% greater than the third number and the second number is 50% greater than the third number. To find the ratio of the two numbers, we can express the first number as 100% + 20% = 120% of the third number, and the second number as 100% + 50% = 150% of the third number. Simplifying these percentages, we get the ratio of the two numbers as 120% : 150%. Dividing both sides by 10, we get the simplified ratio as 12 : 15, which further simplifies to 4 : 5.

Explanation

If two numbers are respectively 20% and 50% more than a third number, it means that the first number is 20% greater than the third number and the second number is 50% greater than the third number. To find the ratio of the two numbers, we can express the first number as 100% + 20% = 120% of the third number, and the second number as 100% + 50% = 150% of the third number. Simplifying these percentages, we get the ratio of the two numbers as 120% : 150%. Dividing both sides by 10, we get the simplified ratio as 12 : 15, which further simplifies to 4 : 5.

46. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

RS 375

Rs 400

Rs 600

Rs 800

A alone can do 1/6th of the work in a day, while B alone can do 1/8th of the work in a day. In 3 days, A and B together completed 3/6 + 3/8 = 7/8th of the work. This means that C completed 1/8th of the work in 3 days. Since the total payment for the work is Rs. 3200, C should be paid 1/8th of Rs. 3200, which is Rs. 400.

Explanation

A alone can do 1/6th of the work in a day, while B alone can do 1/8th of the work in a day. In 3 days, A and B together completed 3/6 + 3/8 = 7/8th of the work. This means that C completed 1/8th of the work in 3 days. Since the total payment for the work is Rs. 3200, C should be paid 1/8th of Rs. 3200, which is Rs. 400.

47. A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:

4

9

12

49

The smaller wheel has 6 cogs and the larger wheel has 14 cogs. This means that for every revolution of the smaller wheel, the larger wheel will make 14/6 revolutions. So, when the smaller wheel has made 21 revolutions, the larger wheel will make 21 * (14/6) = 49 revolutions. Therefore, the correct answer is 49.

Explanation

The smaller wheel has 6 cogs and the larger wheel has 14 cogs. This means that for every revolution of the smaller wheel, the larger wheel will make 14/6 revolutions. So, when the smaller wheel has made 21 revolutions, the larger wheel will make 21 * (14/6) = 49 revolutions. Therefore, the correct answer is 49.

48. At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?

6%

6.50%

7%

7.50%

To find the rate of compound interest, we can use the formula:

Amount = Principal * (1 + Rate/100)^Time

In this case, the principal is Rs. 1200, the amount is Rs. 1348.32, and the time is 2 years. Plugging in these values, we get:

1348.32 = 1200 * (1 + Rate/100)^2

Dividing both sides by 1200, we get:

1.1236 = (1 + Rate/100)^2

Taking the square root of both sides, we get:

1 + Rate/100 = 1.06

Subtracting 1 from both sides, we get:

Rate/100 = 0.06

Multiplying both sides by 100, we get:

Rate = 6%

Therefore, the correct answer is 6%.

Explanation

To find the rate of compound interest, we can use the formula:

Amount = Principal * (1 + Rate/100)^Time

In this case, the principal is Rs. 1200, the amount is Rs. 1348.32, and the time is 2 years. Plugging in these values, we get:

1348.32 = 1200 * (1 + Rate/100)^2

Dividing both sides by 1200, we get:

1.1236 = (1 + Rate/100)^2

Taking the square root of both sides, we get:

1 + Rate/100 = 1.06

Subtracting 1 from both sides, we get:

Rate/100 = 0.06

Multiplying both sides by 100, we get:

Rate = 6%

Therefore, the correct answer is 6%.

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

4

5

6

7

The code initializes an integer variable x with a value of 5 and creates a pointer variable p that points to the memory address of x. The printf statement increments the value stored at the memory address pointed by p by 1 using the prefix increment operator (++). Therefore, the output will be the updated value of x, which is 6.

Explanation

The code initializes an integer variable x with a value of 5 and creates a pointer variable p that points to the memory address of x. The printf statement increments the value stored at the memory address pointed by p by 1 using the prefix increment operator (++). Therefore, the output will be the updated value of x, which is 6.

50. Sometimes we walked through the pine forest as

The path was unaffected by the frost

It was good walking with nails in the boots

The walks was invigorating

It was sheer joy to walk in the forest

The correct answer is that the path was unaffected by the frost. This means that the path was not covered in ice or slippery, making it easier and safer to walk through the pine forest.

Explanation

The correct answer is that the path was unaffected by the frost. This means that the path was not covered in ice or slippery, making it easier and safer to walk through the pine forest.

51. A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:

Rs 120

Rs 121

Rs 122

Rs 123

The bank offers compound interest calculated on a half-yearly basis, which means that interest is added to the principal amount twice a year. The customer deposits Rs. 1600 on 1st January and 1st July, so there are two investment periods in a year.

For the first investment period (January to July), the customer gains interest on Rs. 1600 for 6 months at a rate of 5%. The interest gained in this period is (1600 * 5/100 * 6/12) = Rs. 40.

For the second investment period (July to December), the customer again gains interest on Rs. 1600 for 6 months at a rate of 5%. The interest gained in this period is also (1600 * 5/100 * 6/12) = Rs. 40.

Therefore, at the end of the year, the customer would have gained a total of Rs. 40 + Rs. 40 = Rs. 80 in interest. Adding this to the principal amount, the total amount gained is Rs. 1600 + Rs. 80 = Rs. 1680.

However, the question asks for the amount gained by way of interest only. Therefore, the correct answer is Rs. 80.

Explanation

The bank offers compound interest calculated on a half-yearly basis, which means that interest is added to the principal amount twice a year. The customer deposits Rs. 1600 on 1st January and 1st July, so there are two investment periods in a year.

For the first investment period (January to July), the customer gains interest on Rs. 1600 for 6 months at a rate of 5%. The interest gained in this period is (1600 * 5/100 * 6/12) = Rs. 40.

For the second investment period (July to December), the customer again gains interest on Rs. 1600 for 6 months at a rate of 5%. The interest gained in this period is also (1600 * 5/100 * 6/12) = Rs. 40.

Therefore, at the end of the year, the customer would have gained a total of Rs. 40 + Rs. 40 = Rs. 80 in interest. Adding this to the principal amount, the total amount gained is Rs. 1600 + Rs. 80 = Rs. 1680.

However, the question asks for the amount gained by way of interest only. Therefore, the correct answer is Rs. 80.

52. The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

76 KG

76.5 KG

85 KG

Data Inadequate

None of these

When a new person weighing 65 kg replaces one of the 8 persons, the average weight of the group increases by 2.5 kg. This means that the total weight of the group increases by 2.5 kg multiplied by 8, which is 20 kg. Therefore, the weight of the new person must be 65 kg + 20 kg = 85 kg.

Explanation

When a new person weighing 65 kg replaces one of the 8 persons, the average weight of the group increases by 2.5 kg. This means that the total weight of the group increases by 2.5 kg multiplied by 8, which is 20 kg. Therefore, the weight of the new person must be 65 kg + 20 kg = 85 kg.

53. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:

50 M

72 M

80 M

82 M

The faster train is overtaking the slower train, so the relative speed between the two trains is the difference between their speeds: 46 km/hr - 36 km/hr = 10 km/hr. In 36 seconds, the faster train covers a distance equal to its own length plus the length of the slower train. Let's assume the length of each train is L meters.

The distance covered by the faster train in 36 seconds is (10 km/hr * 36 seconds) / (3600 seconds/hr) = 100 meters.

Therefore, the length of each train is L = 100 meters / 2 = 50 meters.

Hence, the correct answer is 50 M.

Explanation

The faster train is overtaking the slower train, so the relative speed between the two trains is the difference between their speeds: 46 km/hr - 36 km/hr = 10 km/hr. In 36 seconds, the faster train covers a distance equal to its own length plus the length of the slower train. Let's assume the length of each train is L meters.

The distance covered by the faster train in 36 seconds is (10 km/hr * 36 seconds) / (3600 seconds/hr) = 100 meters.

Therefore, the length of each train is L = 100 meters / 2 = 50 meters.

Hence, the correct answer is 50 M.

54. Frozen ruts' means

Very cold roads

Wheel marks in which frost had become hard

The road covered with frost

Hard roads covered with snow

Frozen ruts refer to wheel marks in which frost has become hard. This means that the ruts on the road have been covered with frost, causing them to freeze and become hard. This can make the road surface slippery and difficult to navigate.

Explanation

Frozen ruts refer to wheel marks in which frost has become hard. This means that the ruts on the road have been covered with frost, causing them to freeze and become hard. This can make the road surface slippery and difficult to navigate.

55. The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

15

16

18

25

In this question, the cost price of 20 articles is equal to the selling price of x articles. This means that the selling price of each article is the same. Since the profit is 25%, the selling price is 125% of the cost price. Therefore, the value of x can be calculated by dividing 125% of the cost price of 20 articles by the selling price of each article. Simplifying this equation, we find that x is equal to 16.

Explanation

In this question, the cost price of 20 articles is equal to the selling price of x articles. This means that the selling price of each article is the same. Since the profit is 25%, the selling price is 125% of the cost price. Therefore, the value of x can be calculated by dividing 125% of the cost price of 20 articles by the selling price of each article. Simplifying this equation, we find that x is equal to 16.

56. If a non leap year has two consecutive months with the thirteenth day on Friday, what are the months?

January and February

February and March

March and April

April and May

In a non-leap year, February has 28 days. If the thirteenth day of February falls on a Friday, then the next day, the fourteenth, will be on a Saturday. The next month, March, will start on a Sunday. Therefore, the two consecutive months with the thirteenth day on Friday are February and March.

Explanation

In a non-leap year, February has 28 days. If the thirteenth day of February falls on a Friday, then the next day, the fourteenth, will be on a Saturday. The next month, March, will start on a Sunday. Therefore, the two consecutive months with the thirteenth day on Friday are February and March.

57. Select the lettered pair that has the same relationship as Utopia : English

Odyssey : Greek

Tulsidas : Sanskrit

Dante : Latin

The correct answer is Odyssey : Greek. Just like Utopia is associated with English, Odyssey is associated with Greek. Both Utopia and Odyssey are literary works that are written in their respective languages. Therefore, the relationship between Utopia and English is the same as the relationship between Odyssey and Greek. The other options, Tulsidas : Sanskrit and Dante : Latin, do not have the same relationship as Utopia : English.

Explanation

The correct answer is Odyssey : Greek. Just like Utopia is associated with English, Odyssey is associated with Greek. Both Utopia and Odyssey are literary works that are written in their respective languages. Therefore, the relationship between Utopia and English is the same as the relationship between Odyssey and Greek. The other options, Tulsidas : Sanskrit and Dante : Latin, do not have the same relationship as Utopia : English.

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

810

1440

2880

50400

5760

The word 'CORPORATION' has 11 letters, including 5 vowels (O, O, A, I, O). To arrange the letters such that the vowels always come together, we can treat the group of vowels (OOAIO) as one entity. This entity can be arranged in 5! = 120 ways. The remaining 6 letters (C, R, P, R, T, N) can be arranged in 6! = 720 ways. Therefore, the total number of arrangements is 120 * 720 = 86,400. However, since the two 'O' letters are repeated, we need to divide by 2! = 2 to account for the overcounting. Hence, the final answer is 86,400 / 2 = 43,200.

Explanation

The word 'CORPORATION' has 11 letters, including 5 vowels (O, O, A, I, O). To arrange the letters such that the vowels always come together, we can treat the group of vowels (OOAIO) as one entity. This entity can be arranged in 5! = 120 ways. The remaining 6 letters (C, R, P, R, T, N) can be arranged in 6! = 720 ways. Therefore, the total number of arrangements is 120 * 720 = 86,400. However, since the two 'O' letters are repeated, we need to divide by 2! = 2 to account for the overcounting. Hence, the final answer is 86,400 / 2 = 43,200.

59. What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?

196

630

1260

2520

To find the least number that is divisible by 12, 18, 21, and 30 when doubled, we need to find the least common multiple (LCM) of these numbers. The LCM of 12, 18, 21, and 30 is 1260. When this number is doubled, we get 2520. However, this is not the least number that satisfies the condition. The next multiple of 1260 is 3780, which is not necessary to consider. Therefore, the least number that when doubled is divisible by 12, 18, 21, and 30 is 1260.

Explanation

To find the least number that is divisible by 12, 18, 21, and 30 when doubled, we need to find the least common multiple (LCM) of these numbers. The LCM of 12, 18, 21, and 30 is 1260. When this number is doubled, we get 2520. However, this is not the least number that satisfies the condition. The next multiple of 1260 is 3780, which is not necessary to consider. Therefore, the least number that when doubled is divisible by 12, 18, 21, and 30 is 1260.

60. How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

5

10

15

20

To form a 3-digit number that is divisible by 5, the units digit has to be either 5 or 0. Since none of the digits can be repeated, there are 2 choices for the units digit. For the hundreds digit, any of the remaining 4 digits can be chosen. And for the tens digit, any of the remaining 3 digits can be chosen. Therefore, the total number of 3-digit numbers that can be formed is 2 choices for the units digit multiplied by 4 choices for the hundreds digit multiplied by 3 choices for the tens digit, which equals 2 x 4 x 3 = 24. But since one of the choices for the hundreds digit is 0, which would make the number a 2-digit number, we have to subtract 4 from the total. Therefore, the correct answer is 20.

Explanation

To form a 3-digit number that is divisible by 5, the units digit has to be either 5 or 0. Since none of the digits can be repeated, there are 2 choices for the units digit. For the hundreds digit, any of the remaining 4 digits can be chosen. And for the tens digit, any of the remaining 3 digits can be chosen. Therefore, the total number of 3-digit numbers that can be formed is 2 choices for the units digit multiplied by 4 choices for the hundreds digit multiplied by 3 choices for the tens digit, which equals 2 x 4 x 3 = 24. But since one of the choices for the hundreds digit is 0, which would make the number a 2-digit number, we have to subtract 4 from the total. Therefore, the correct answer is 20.

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

Imile

Mile

Fasci

Fasc

The code is using pointer arithmetic by adding 5 to the address of the string "Fascimile". This means that it will start printing the characters from the 5th index of the string, which is "mile". Therefore, the output will be "mile".

Explanation

The code is using pointer arithmetic by adding 5 to the address of the string "Fascimile". This means that it will start printing the characters from the 5th index of the string, which is "mile". Therefore, the output will be "mile".

62. A man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%, his annual income is:

Rs 205.40

Rs 534.60

Rs 648

Rs 655.60

The man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. This means he bought 4455/8.25 = 540 shares. The rate of dividend is 12%, so his annual income from these shares would be 540 * 10 * 0.12 = Rs. 648. Therefore, the correct answer is Rs. 648.

Explanation

The man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. This means he bought 4455/8.25 = 540 shares. The rate of dividend is 12%, so his annual income from these shares would be 540 * 10 * 0.12 = Rs. 648. Therefore, the correct answer is Rs. 648.

63. A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is:

7.50%

8%

9.70%

None of These

The dividend from the stock can be calculated by dividing the income obtained from the investment by the amount invested and then multiplying the result by 100. In this case, the income obtained is Rs. 128 and the amount invested is Rs. 1552. So, (128/1552) * 100 = 8%. Therefore, the dividend from the stock is 8%.

Explanation

The dividend from the stock can be calculated by dividing the income obtained from the investment by the amount invested and then multiplying the result by 100. In this case, the income obtained is Rs. 128 and the amount invested is Rs. 1552. So, (128/1552) * 100 = 8%. Therefore, the dividend from the stock is 8%.

64. A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

18 DAYS

24 DAYS

30 DAYS

36 DAYS

A, B, and C have different rates of work. Let's assume that A's rate is x units per day, B's rate is y units per day, and C's rate is z units per day. From the given information, we can form the following equations:

1) (x + y) * 30 = 1 (work done by A and B in 30 days)
2) (y + z) * 24 = 1 (work done by B and C in 24 days)
3) (z + x) * 20 = 1 (work done by C and A in 20 days)

Solving these equations, we find that x = 1/60, y = 1/120, and z = 1/240.

In 10 days, A, B, and C together complete (1/60 + 1/120 + 1/240) * 10 = 1/6 of the work.

Now, A is left alone to complete the remaining 5/6 of the work. Since A's rate is 1/60 units per day, it will take A (5/6) / (1/60) = 50 days to finish the work.

Therefore, A will take 50 - 10 = 40 more days to finish the work.

The correct answer is 40 days, which is not provided in the options.

Explanation

A, B, and C have different rates of work. Let's assume that A's rate is x units per day, B's rate is y units per day, and C's rate is z units per day. From the given information, we can form the following equations:

1) (x + y) * 30 = 1 (work done by A and B in 30 days)
2) (y + z) * 24 = 1 (work done by B and C in 24 days)
3) (z + x) * 20 = 1 (work done by C and A in 20 days)

Solving these equations, we find that x = 1/60, y = 1/120, and z = 1/240.

In 10 days, A, B, and C together complete (1/60 + 1/120 + 1/240) * 10 = 1/6 of the work.

Now, A is left alone to complete the remaining 5/6 of the work. Since A's rate is 1/60 units per day, it will take A (5/6) / (1/60) = 50 days to finish the work.

Therefore, A will take 50 - 10 = 40 more days to finish the work.

The correct answer is 40 days, which is not provided in the options.

65. 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

9

10

11

12

If 3 pumps working 8 hours a day can empty the tank in 2 days, it means that each pump can empty 1/3 of the tank in 2 days. Therefore, each pump can empty 1/6 of the tank in 1 day. To empty the tank in 1 day, we need 4 pumps working. Since each pump can empty 1/6 of the tank in 1 day, 4 pumps can empty 4/6 or 2/3 of the tank in 1 day. This means that 4 pumps need to work for 2/3 of a day or 16 hours. However, since we are looking for the number of hours a day, we round this up to the nearest whole number, which is 12 hours.

Explanation

If 3 pumps working 8 hours a day can empty the tank in 2 days, it means that each pump can empty 1/3 of the tank in 2 days. Therefore, each pump can empty 1/6 of the tank in 1 day. To empty the tank in 1 day, we need 4 pumps working. Since each pump can empty 1/6 of the tank in 1 day, 4 pumps can empty 4/6 or 2/3 of the tank in 1 day. This means that 4 pumps need to work for 2/3 of a day or 16 hours. However, since we are looking for the number of hours a day, we round this up to the nearest whole number, which is 12 hours.

66. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:

9

11

13

15

Let's assume the first odd integer is x. The second odd integer would be x+2 and the third odd integer would be x+4. According to the given information, 3 times the first integer (3x) is equal to 3 more than twice the third integer (2(x+4)+3). Simplifying this equation, we get 3x = 2x + 8 + 3. Solving for x, we find that x = 11. Therefore, the third integer is x+4 = 11+4 = 15.

Explanation

Let's assume the first odd integer is x. The second odd integer would be x+2 and the third odd integer would be x+4. According to the given information, 3 times the first integer (3x) is equal to 3 more than twice the third integer (2(x+4)+3). Simplifying this equation, we get 3x = 2x + 8 + 3. Solving for x, we find that x = 11. Therefore, the third integer is x+4 = 11+4 = 15.

67. How many times in a day, are the hands of a clock in straight line but opposite in direction?

20

22

24

48

The hour and minute hands of a clock are in a straight line but opposite in direction 11 times in a 12-hour period. Since there are 24 hours in a day, the hands of a clock will be in a straight line but opposite in direction 22 times in a day.

Explanation

The hour and minute hands of a clock are in a straight line but opposite in direction 11 times in a 12-hour period. Since there are 24 hours in a day, the hands of a clock will be in a straight line but opposite in direction 22 times in a day.

68. A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

230 M

240 M

260 M

320 M

None of these

When two trains are moving towards each other, their relative speed is the sum of their individual speeds. In this case, the relative speed is 120 kmph + 80 kmph = 200 kmph. To convert this to meters per second, we divide by 3.6 (since 1 kmph = 1000 m/3600 s). Therefore, the relative speed is 200 kmph / 3.6 = 55.56 m/s. The length of the train being crossed is equal to the distance traveled by the first train in the time it takes to cross the other train. The distance traveled by the first train is equal to its speed multiplied by the time taken, which is 55.56 m/s * 9 s = 500 m. Therefore, the length of the other train is 500 m - 270 m (length of the first train) = 230 m.

Explanation

When two trains are moving towards each other, their relative speed is the sum of their individual speeds. In this case, the relative speed is 120 kmph + 80 kmph = 200 kmph. To convert this to meters per second, we divide by 3.6 (since 1 kmph = 1000 m/3600 s). Therefore, the relative speed is 200 kmph / 3.6 = 55.56 m/s. The length of the train being crossed is equal to the distance traveled by the first train in the time it takes to cross the other train. The distance traveled by the first train is equal to its speed multiplied by the time taken, which is 55.56 m/s * 9 s = 500 m. Therefore, the length of the other train is 500 m - 270 m (length of the first train) = 230 m.

69. The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:

Zero Dregrees

10 Degrees

5 Degrees

20 Degrees

At 4:20, the minute hand is at the 4 on the clock, while the hour hand is slightly past the 4. The hour hand moves 30 degrees per hour, so at 4:20, it has moved 20/60 * 30 = 10 degrees. Therefore, the angle between the minute hand and the hour hand is 10 degrees.

Explanation

At 4:20, the minute hand is at the 4 on the clock, while the hour hand is slightly past the 4. The hour hand moves 30 degrees per hour, so at 4:20, it has moved 20/60 * 30 = 10 degrees. Therefore, the angle between the minute hand and the hour hand is 10 degrees.

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

ABC+DE/*-

ABCDE+*/-

A+E-(B+C)*D

None of These

The given expression is in infix notation, where operators are placed between the operands. To convert it to postfix notation, we start by scanning the expression from left to right. Each time we encounter an operand, we output it directly. When we encounter an operator, we push it onto a stack, unless there is an operator with higher precedence on top of the stack. In that case, we pop the higher precedence operator and output it, then push the current operator onto the stack. After scanning the entire expression, we pop all remaining operators from the stack and output them. The resulting postfix expression for A-(B+C)*(D/E) is ABC+DE/*-.

Explanation

The given expression is in infix notation, where operators are placed between the operands. To convert it to postfix notation, we start by scanning the expression from left to right. Each time we encounter an operand, we output it directly. When we encounter an operator, we push it onto a stack, unless there is an operator with higher precedence on top of the stack. In that case, we pop the higher precedence operator and output it, then push the current operator onto the stack. After scanning the entire expression, we pop all remaining operators from the stack and output them. The resulting postfix expression for A-(B+C)*(D/E) is ABC+DE/*-.

71. 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. Then, it checks if x is equal to 0 using the if statement. Since x is indeed equal to 0, the code executes the printf statement "hi". After that, it reaches the printf statement "hello" which is not inside any conditional statement and will always be executed. Therefore, the output of this code will be "hi" followed by "hello".

Explanation

The code starts by initializing the variable x to 0. Then, it checks if x is equal to 0 using the if statement. Since x is indeed equal to 0, the code executes the printf statement "hi". After that, it reaches the printf statement "hello" which is not inside any conditional statement and will always be executed. Therefore, the output of this code will be "hi" followed by "hello".

72. The floor of the forest was soft because

The forest did not harden it on account of trees

The travellers were wearing boots

The shoes had nails on their sole and heel

They enjoyed walking in the woods

The floor of the forest was soft because the trees in the forest did not compact the soil or make it hard.

Explanation

The floor of the forest was soft because the trees in the forest did not compact the soil or make it hard.

73. In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C:

8 points

10 points

14 points

40 points

If A can give B 20 points and C 28 points, it means that A is better than both B and C in the game. Therefore, B must be better than C. Since the difference between the points given by A to B and C is 8 (28-20), the difference between the points B can give to C must also be 8. Hence, B can give C 10 points.

Explanation

If A can give B 20 points and C 28 points, it means that A is better than both B and C in the game. Therefore, B must be better than C. Since the difference between the points given by A to B and C is 8 (28-20), the difference between the points B can give to C must also be 8. Hence, B can give C 10 points.

74. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:

4

5

6

8

The greatest number that will divide 1305, 4665, and 6905, leaving the same remainder in each case is the greatest common divisor (GCD) of these three numbers. To find the GCD, we can use the Euclidean algorithm. Dividing 4665 by 1305 gives a quotient of 3 and a remainder of 750. Dividing 1305 by 750 gives a quotient of 1 and a remainder of 555. Finally, dividing 750 by 555 gives a quotient of 1 and a remainder of 195. Therefore, the GCD of 1305, 4665, and 6905 is 195. The sum of the digits in 195 is 1 + 9 + 5 = 15, which reduces to 1 + 5 = 6.

Explanation

The greatest number that will divide 1305, 4665, and 6905, leaving the same remainder in each case is the greatest common divisor (GCD) of these three numbers. To find the GCD, we can use the Euclidean algorithm. Dividing 4665 by 1305 gives a quotient of 3 and a remainder of 750. Dividing 1305 by 750 gives a quotient of 1 and a remainder of 555. Finally, dividing 750 by 555 gives a quotient of 1 and a remainder of 195. Therefore, the GCD of 1305, 4665, and 6905 is 195. The sum of the digits in 195 is 1 + 9 + 5 = 15, which reduces to 1 + 5 = 6.

75. The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?

69

78

96

Cannot be determined

None of these

not-available-via-ai

Explanation

not-available-via-ai

76. A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?

11:30 A.M.

12 noon

12:30 P.M.

1:00 P.M.

Machine P can print 1 lakh books in 8 hours, which means it can print 12,500 books per hour. Machine Q can print the same number of books in 10 hours, so it can print 10,000 books per hour. Machine R can print 1 lakh books in 12 hours, which means it can print 8,333 books per hour.

Machine P is closed at 11 A.M., which means it has worked for 2 hours. In these 2 hours, it would have printed 25,000 books.

The remaining work of 75,000 books will be completed by machines Q and R. Together, they can print 18,333 books per hour.

To print 75,000 books at this rate, it will take approximately 4.1 hours.

Adding this to the time when machine P was closed (2 hours), the work will be finished at approximately 1:00 P.M.

Explanation

Machine P can print 1 lakh books in 8 hours, which means it can print 12,500 books per hour. Machine Q can print the same number of books in 10 hours, so it can print 10,000 books per hour. Machine R can print 1 lakh books in 12 hours, which means it can print 8,333 books per hour.

Machine P is closed at 11 A.M., which means it has worked for 2 hours. In these 2 hours, it would have printed 25,000 books.

The remaining work of 75,000 books will be completed by machines Q and R. Together, they can print 18,333 books per hour.

To print 75,000 books at this rate, it will take approximately 4.1 hours.

Adding this to the time when machine P was closed (2 hours), the work will be finished at approximately 1:00 P.M.

77. A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

66 KMPH

72 KMPH

78 KMPH

81 KMPH

When the train overtakes the first person, it covers a distance equal to its own length plus the distance the person has walked in 8.4 seconds. Similarly, when the train overtakes the second person, it covers a distance equal to its own length plus the distance the person has walked in 8.5 seconds.

Let's assume the length of the train is 'x' km.

For the first person, the distance covered by the train is x + (4.5 * (8.4/3600)) km.
For the second person, the distance covered by the train is x + (5.4 * (8.5/3600)) km.

Since the train takes the same amount of time to overtake both persons, we can equate the two distances.

x + (4.5 * (8.4/3600)) = x + (5.4 * (8.5/3600))

Simplifying the equation, we get:

(4.5 * (8.4/3600)) = (5.4 * (8.5/3600))

Solving for x, we find that x = 0.3 km.

Therefore, the length of the train is 0.3 km and the speed of the train is the distance covered in 8.4 seconds, which is (0.3 * 3600)/8.4 = 81 km/hr.

Explanation

When the train overtakes the first person, it covers a distance equal to its own length plus the distance the person has walked in 8.4 seconds. Similarly, when the train overtakes the second person, it covers a distance equal to its own length plus the distance the person has walked in 8.5 seconds.

Let's assume the length of the train is 'x' km.

For the first person, the distance covered by the train is x + (4.5 * (8.4/3600)) km.
For the second person, the distance covered by the train is x + (5.4 * (8.5/3600)) km.

Since the train takes the same amount of time to overtake both persons, we can equate the two distances.

x + (4.5 * (8.4/3600)) = x + (5.4 * (8.5/3600))

Simplifying the equation, we get:

(4.5 * (8.4/3600)) = (5.4 * (8.5/3600))

Solving for x, we find that x = 0.3 km.

Therefore, the length of the train is 0.3 km and the speed of the train is the distance covered in 8.4 seconds, which is (0.3 * 3600)/8.4 = 81 km/hr.

78. If Rs. 10 be allowed as true discount on a bill of Rs. 110 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:

Rs 20

Rs 21.81

Rs 22

Rs 18.33

The true discount is the difference between the face value of the bill and the amount paid. In this case, the face value of the bill is Rs. 110 and the true discount is Rs. 10. Therefore, the amount paid is Rs. 100.

If the time period is doubled, the amount due at the end of double the time will also be doubled. So, the amount due will be Rs. 200.

To find the discount allowed on this amount, we can use the formula:

Discount = (True Discount * Amount Due) / Face Value

Substituting the values, we get:

Discount = (10 * 200) / 110 = Rs. 18.33

Therefore, the discount allowed on the same sum due at the end of double the time is Rs. 18.33.

Explanation

The true discount is the difference between the face value of the bill and the amount paid. In this case, the face value of the bill is Rs. 110 and the true discount is Rs. 10. Therefore, the amount paid is Rs. 100.

If the time period is doubled, the amount due at the end of double the time will also be doubled. So, the amount due will be Rs. 200.

To find the discount allowed on this amount, we can use the formula:

Discount = (True Discount * Amount Due) / Face Value

Substituting the values, we get:

Discount = (10 * 200) / 110 = Rs. 18.33

Therefore, the discount allowed on the same sum due at the end of double the time is Rs. 18.33.

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

1235689

123456789

12345678910

None of These

not-available-via-ai

Explanation

not-available-via-ai

80. . 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 output of the code is "how are your" because the variable "x" is not initialized or given a value. Therefore, the condition "if (x)" will evaluate to false, and the code will execute the else statement, which prints "how are you".

Explanation

The output of the code is "how are your" because the variable "x" is not initialized or given a value. Therefore, the condition "if (x)" will evaluate to false, and the code will execute the else statement, which prints "how are you".

81. We found great joy on account of

Wearing nailed boots

The good long walk on the road

Walking occasionally through the forest

Walking on frost with nailed boots on

Walking on frost with nailed boots on can bring great joy because it provides a unique and exhilarating experience. The nails on the boots provide traction and stability on the icy surface, allowing for a confident and secure walk. The crunching sound of the boots on the frost adds to the sensory experience, creating a sense of adventure and excitement. Additionally, the beauty of the frost-covered landscape and the refreshing cold air can enhance the joy of the walk.

Explanation

Walking on frost with nailed boots on can bring great joy because it provides a unique and exhilarating experience. The nails on the boots provide traction and stability on the icy surface, allowing for a confident and secure walk. The crunching sound of the boots on the frost adds to the sensory experience, creating a sense of adventure and excitement. Additionally, the beauty of the frost-covered landscape and the refreshing cold air can enhance the joy of the walk.

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

00001111

00011010

00011110

00011111

The correct binary representation for the decimal value 30 is 00011111. In binary, each digit can have a value of either 0 or 1, and the value of each digit increases by a power of 2 as you move from right to left. Therefore, the binary representation of 30 is obtained by adding the binary values for 16, 8, 4, 2, and 0, which gives us 00011111.

Explanation

The correct binary representation for the decimal value 30 is 00011111. In binary, each digit can have a value of either 0 or 1, and the value of each digit increases by a power of 2 as you move from right to left. Therefore, the binary representation of 30 is obtained by adding the binary values for 16, 8, 4, 2, and 0, which gives us 00011111.

83. Tanya is older than Eric. Cliff is older than Tanya. Eric is older than Cliff. If the first two statements are true, the third statement is

1

UNCERTAIN

If the first two statements are true, then it implies that Tanya is older than Eric, and Cliff is older than Tanya. Therefore, based on the given information, it is certain that Eric is older than Cliff.

Explanation

If the first two statements are true, then it implies that Tanya is older than Eric, and Cliff is older than Tanya. Therefore, based on the given information, it is certain that Eric is older than Cliff.