1.
Modern economies does not differentiate between renewable and non-renewable materials, as its method is to measures everything by means of a money price. Thus, taking various alternatives fuels, like coal, oil, wood or water power: the only difference between them recognised by modern economics is relative cost per equivalent unit. The cheapest is automatically the one to be preferred, as to do otherwise would be irrational and 'uneconomic'. From a Buddhist point of view of course this will not do, the essential difference between non-renewable fuels like coal and oil on the one hand and renewable fuels like wood and water power on the other cannot be simply overlooked. Non-renewable goods must be used only if they are indespensible, and then only with the greatest care and the highest concern for conservation. To use them carelessly or extravagantly is an act of violence, and while complete non-violence may not be possible on earth, it is nonetheless the duty of man to aim at deal of non-violence in all he does.
2.
Write and Essay about " Your Most Memorable day in College "
3.
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?
Correct Answer
C. 21
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.
4.
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?
Correct Answer
A. Rs. 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.
5.
The true discount on a bill of Rs. 540 is Rs. 90. The banker's discount is:
Correct Answer
B. 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.
6.
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:
Correct Answer
B. 5
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.
7.
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:
Correct Answer
A. 2 MpH
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.
8.
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:
Correct Answer
B. 3 : 1
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.
9.
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?
Correct Answer
B. 13
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.
10.
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?
Correct Answer
B. 30
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.
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?
Correct Answer
D. 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.
How many times are the hands of a clock at right angle in a day?
Correct Answer
C. 44
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.
13.
How many times in a day, the hands of a clock are straight?
Correct Answer
C. 44
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.
14.
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?
Correct Answer
C. Rs 3972
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.
15.
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?
Correct Answer
C. Rs 8820
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.
16.
The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:
Correct Answer
B. 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.
17.
From a point P on a level ground, the angle of elevation of the top tower is 30Âº. If the tower is 100 m high, the distance of point P from the foot of the tower is:
Correct Answer
C. 173 m
Explanation
The angle of elevation of 30Âº 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 30Âº 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.
18.
If 20% of a = b, then b% of 20 is the same as:
Correct Answer
A. 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.
19.
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?
Correct Answer
B. RS 250
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.
20.
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?
Correct Answer
D. 756
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.
21.
In how many ways can the letters of the word 'LEADER' be arranged?
Correct Answer
C. 360
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.
22.
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
Correct Answer
C. 64
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.
23.
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
Correct Answer
C. 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.
24.
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?
Correct Answer
D. 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.
25.
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:
Correct Answer
D. 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.
26.
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
Correct Answer
C. 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.
27.
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:
Correct Answer
C. 322
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.
28.
The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:
Correct Answer
C. 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.
29.
The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:
Correct Answer
D. 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.
30.
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 ?
Correct Answer
D. 46 minutes and 12 seconds
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.
31.
The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
Correct Answer
B. 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.
32.
Find the highest common factor of 36 and 84.
Correct Answer
C. 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.
33.
The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:
Correct Answer
C. 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.
34.
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 ?
Correct Answer
B. 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.
35.
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:
Correct Answer
D. 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.
36.
The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:
Correct Answer
B. 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.
37.
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Correct Answer
D. 150 METRES
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.
38.
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?
Correct Answer
B. 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.
39.
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:
Correct Answer
C. 48
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.
40.
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:
Correct Answer
C. 60 kmpH
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 Ã— time, so we can write the equation as 200 = (x + 2x) Ã— 8.
Simplifying the equation, we get 200 = 3x Ã— 8.
Dividing both sides by 24, we find x = 25.
Therefore, the speed of the faster train is 2x = 2 Ã— 25 = 50 km/h.
Hence, the correct answer is 60 km/h.
41.
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:
Correct Answer
C. 500
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.
42.
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?
Correct Answer
B. 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.
43.
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:
Correct Answer
D. 82 KMpH
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.
44.
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?
Correct Answer
B. 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.
45.
A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?
Correct Answer
C. 5
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%.
46.
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?
Correct Answer
C. 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.
47.
In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:
Correct Answer
B. 20m
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.
48.
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?
Correct Answer
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.
49.
In a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is:
Correct Answer
B. 80 sec
50.
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?
Correct Answer
A. 2 : 3 : 4
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.