1.
The greatest thing this age can be proud of is the birth of man in the consciousness of men. In his drunken orgies of power and national pride man may flout and jeer at it. when organised national selfishness, racial antipathy and commercial self seeking begin to display their ugly deformities in all their nakedness, then comes the time for man to know that his salvation is not in political organisations and extended trade relations, not in any mechanical re-arrangement of social system but in a deeper transformation of life, in the liberation of consciousness in love, in the realization of God in man
2.
Write a paragraph on " Where you would like to see yourself in 5 years from now ? "
3.
Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
Correct Answer
C. Rs175.50
Explanation
Let the price of the third variety be Rs. x per kg. Since the ratio of the first variety to the second variety to the third variety is 1:1:2, we can set up the following equation: (126 + 135 + 2x)/4 = 153. Solving this equation, we get 261 + 2x = 612. Simplifying further, we find that 2x = 351. Dividing both sides by 2, we get x = 175.50. Therefore, the price of the third variety per kg is Rs. 175.50.
4.
In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
Correct Answer
A. 6.25
Explanation
To find the required run rate for the remaining 40 overs, we need to calculate the total runs required in those overs. Since the first 10 overs had a run rate of 3.2, the total runs scored in those overs would be 10 * 3.2 = 32. Therefore, the remaining runs required to reach the target of 282 would be 282 - 32 = 250. To calculate the run rate, we divide the remaining runs by the number of overs, which gives us 250 / 40 = 6.25. Therefore, the required run rate in the remaining 40 overs to reach the target is 6.25.
5.
The present worth of a sum due sometime hence is Rs. 576 and the banker's gain is Rs. 16. The true discount is:
Correct Answer
D. RS 96
Explanation
The present worth of a sum due sometime hence is Rs. 576 and the banker's gain is Rs. 16. The true discount can be calculated by subtracting the banker's gain from the present worth. Therefore, the true discount is Rs. 576 - Rs. 16 = Rs. 560.
6.
A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
Correct Answer
C. 8 : 3
Explanation
The ratio between the speed of the boat and the speed of the water current can be determined by using the concept of relative speed. Let the speed of the boat be B and the speed of the water current be C. When the boat is running upstream, the effective speed is B - C, and when it is running downstream, the effective speed is B + C. We can set up the following equation based on the given information: (B - C) * 8.8 = (B + C) * 4. Solving this equation, we find that B/C = 8/3, which gives us the ratio between the speed of the boat and the speed of the water current as 8:3.
7.
The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is:
Correct Answer
D. 3.6 KM
Explanation
The speed of the boat in still water is given as 15 km/hr and the rate of the current is 3 km/hr. When the boat is moving downstream, the speed of the boat relative to the ground is the sum of the speed of the boat in still water and the rate of the current, which is 15 km/hr + 3 km/hr = 18 km/hr.
To find the distance traveled downstream in 12 minutes, we need to convert the time to hours. There are 60 minutes in an hour, so 12 minutes is equal to 12/60 = 0.2 hours.
The distance traveled downstream is given by the formula: distance = speed x time. Plugging in the values, we get: distance = 18 km/hr x 0.2 hr = 3.6 km.
Therefore, the distance traveled downstream in 12 minutes is 3.6 km.
8.
Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:
Correct Answer
D. 24 HRS
Explanation
The speed of the boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. When the boat is rowing upstream against the stream, its effective speed is reduced by the speed of the stream, so the speed is 9 - 1.5 = 7.5 kmph. When the boat is rowing downstream with the stream, its effective speed is increased by the speed of the stream, so the speed is 9 + 1.5 = 10.5 kmph. The total distance traveled by the man is 105 km, so the total time taken is 105 / (7.5 + 10.5) = 105 / 18 = 5.83 hours. Since the man also has to row back to the starting point, the total time taken is 5.83 hours x 2 = 11.67 hours, which is approximately 12 hours. Therefore, the correct answer is 24 hours.
9.
Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
Correct Answer
B. 1800
Explanation
If 6 identical machines can produce 270 bottles per minute, then each machine can produce 270/6 = 45 bottles per minute. Therefore, in 4 minutes, each machine can produce 45 x 4 = 180 bottles. Since there are 10 machines, the total number of bottles produced in 4 minutes by 10 machines is 180 x 10 = 1800 bottles.
10.
A flagstaff 17.5 m high casts a shadow of length 40.25 m. The height of the building, which casts a shadow of length 28.75 m under similar conditions will be:
Correct Answer
B. 12.5 m
Explanation
The flagstaff and the building are similar triangles since they are both casting shadows under similar conditions. The ratio of the height of the flagstaff to its shadow is the same as the ratio of the height of the building to its shadow. Therefore, we can set up a proportion: (17.5 m / 40.25 m) = (x / 28.75 m). Solving for x, we find that x is approximately 12.5 m. Therefore, the height of the building is 12.5 m.
11.
4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?
Correct Answer
D. 16
Explanation
If 4 mat-weavers can weave 4 mats in 4 days, it means that each mat-weaver can weave 1 mat in 4 days. Therefore, if there are 8 mat-weavers, they can weave 8 mats in 4 days. Since the rate of weaving is the same, in 8 days, they would be able to weave double the number of mats, which is 16.
12.
At 3:40, the hour hand and the minute hand of a clock form an angle of:
Correct Answer
C. 130 Degrees
Explanation
At 3:40, the minute hand is at the 8-minute mark and the hour hand is slightly past the 3, closer to the 4. The hour hand moves 30 degrees per hour, so at 3:40 it has moved (40/60) * 30 = 20 degrees. The minute hand moves 360 degrees in 60 minutes, so at 3:40 it has moved (8/60) * 360 = 48 degrees. The angle between the hour and minute hand is the difference between their positions, which is 48 - 20 = 28 degrees. Therefore, the correct answer is 130 degrees, as it is the closest option to 28 degrees.
13.
How many times do the hands of a clock coincide in a day?
Correct Answer
C. 22
Explanation
The hour hand of a clock makes a full revolution in 12 hours, while the minute hand completes a full revolution in 60 minutes. Therefore, the hands of a clock coincide when the minute hand catches up to or overtakes the hour hand. This occurs 11 times in the first 12 hours, and another 11 times in the second 12 hours, resulting in a total of 22 coincidences in a day.
14.
The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:
Correct Answer
A. 625
Explanation
The difference between simple and compound interest is given as Re. 1. This means that the compound interest is Re. 1 more than the simple interest. The formula for simple interest is P * R * T / 100, where P is the principal amount, R is the rate of interest, and T is the time period. We can set up the equation P * 4 * 2 / 100 - P * 4 * 2 / 100 = 1. Solving this equation, we find that P = 625. Therefore, the sum of money is Rs. 625.
15.
The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:
Correct Answer
B. 4
Explanation
To calculate the least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled, we need to find the number of years it takes for the amount to reach or exceed twice the initial sum. Since the interest is compounded annually, the amount will double after 5 years (20% interest compounded annually for 5 years will result in a doubling of the initial sum). However, the question asks for the least number of complete years, so the correct answer is 4.
16.
If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?
Correct Answer
A. Rs 51.25
17.
The angle of elevation of a ladder leaning against a wall is 60Âº and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
Correct Answer
D. 9.2 m
Explanation
The angle of elevation of the ladder leaning against the wall is given as 60Âº. This means that the ladder forms a right-angled triangle with the wall and the ground. The length of the ladder is the hypotenuse of this triangle. The foot of the ladder is 4.6 m away from the wall, which is the base of the triangle. Using trigonometry, we can find the length of the ladder by using the sine function: sin(60Âº) = opposite/hypotenuse. Solving for the hypotenuse, we get hypotenuse = opposite/sin(60Âº) = 4.6 m/sin(60Âº) â‰ˆ 9.2 m. Therefore, the length of the ladder is 9.2 m.
18.
What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
Correct Answer
C. 20
Explanation
20% of the numbers from 1 to 70 have 1 or 9 in the unit's digit. To find this percentage, we need to count the numbers from 1 to 70 that have 1 or 9 in the unit's digit and divide it by the total number of numbers from 1 to 70. The numbers with 1 or 9 in the unit's digit are 1, 9, 11, 19, 21, 29, ..., 61, 69. There are 7 numbers with 1 or 9 in the unit's digit. So, the percentage is 7/70 = 0.1 or 10%. However, the question asks for the percentage of numbers with 1 or 9 in the unit's digit, so we need to double this percentage since there are two digits (1 and 9) that satisfy the condition. Therefore, the correct answer is 20%.
19.
Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
Correct Answer
A. 57%
Explanation
The winning candidate received 11628 votes out of a total of (1136+7636+11628) = 20400 votes. To find the percentage, we divide the winning candidate's votes by the total votes and multiply by 100. So, the winning candidate received (11628/20400) * 100 = 57% of the total votes.
20.
The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:
Correct Answer
B. 5%
Explanation
To find the average percent increase of the population per year, we need to calculate the total percent increase over the decade and then divide it by 10. The initial population is 1,75,000 and the final population is 2,62,500. The total increase in population is 2,62,500 - 1,75,000 = 87,500. To find the percent increase, we divide the total increase by the initial population: 87,500 / 1,75,000 = 0.5. Finally, we divide the percent increase by 10 to get the average percent increase per year: 0.5 / 10 = 0.05 or 5%.
21.
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Correct Answer
C. 25200
Explanation
To find the number of words that can be formed with 3 consonants and 2 vowels, we need to calculate the number of ways to choose the consonants and vowels separately, and then multiply those two numbers together.
The number of ways to choose 3 consonants out of 7 is given by the combination formula C(7, 3) = 7! / (3! * (7-3)!) = 35.
Similarly, the number of ways to choose 2 vowels out of 4 is given by C(4, 2) = 4! / (2! * (4-2)!) = 6.
Multiplying these two numbers together gives us 35 * 6 = 210.
However, this only gives us the number of ways to choose the letters, not the number of actual words that can be formed. Since the order of the letters matters, we need to consider the permutations as well.
There are 3 consonants, so there are 3! = 6 ways to arrange them. Similarly, there are 2 vowels, so there are 2! = 2 ways to arrange them.
Multiplying these two numbers together gives us 6 * 2 = 12.
Finally, multiplying the number of ways to choose the letters (210) by the number of ways to arrange them (12) gives us the total number of words that can be formed: 210 * 12 = 25200.
Therefore, the correct answer is 25200.
22.
In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
Correct Answer
C. 11760
Explanation
The question asks how many ways a committee can be formed from a group of 8 men and 10 women. Since the committee consists of 5 men and 6 women, we need to choose 5 men from the 8 available and 6 women from the 10 available. The number of ways to choose k items from a set of n items is given by the combination formula nCk = n! / (k!(n-k)!). Therefore, the number of ways to form the committee is 8C5 * 10C6 = (8! / (5!(8-5)!)) * (10! / (6!(10-6)!)) = 56 * 210 = 11,760.
23.
How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
Correct Answer
C. 5040
Explanation
The word 'LOGARITHMS' has 10 letters. We need to form 4-letter words without repetition. The number of ways to select the first letter is 10. After selecting the first letter, we have 9 letters left to choose from for the second letter. Similarly, we have 8 choices for the third letter and 7 choices for the fourth letter. Therefore, the total number of 4-letter words without repetition is 10 * 9 * 8 * 7 = 5040.
24.
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
Correct Answer
A. 14 Years
Explanation
The father's age at the time of the son's birth was 38 years. Since the father stated that he was as old as the son is now at the time of the son's birth, it means that the son's current age is 38 years. Therefore, five years back, the son's age would have been 38 - 5 = 33 years.
25.
Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
Correct Answer
A. 16 Years
26.
The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
Correct Answer
B. 16 , 28 , 36
Explanation
The present ages of the three persons are in the ratio 4:7:9. Let's assume the ages of the three persons to be 4x, 7x, and 9x respectively.
Eight years ago, their ages would have been (4x-8), (7x-8), and (9x-8) respectively.
According to the given information, the sum of their ages eight years ago was 56.
So, (4x-8) + (7x-8) + (9x-8) = 56.
Simplifying the equation, we get 20x = 80.
Dividing both sides by 20, we find x = 4.
Therefore, the present ages of the three persons are 4x = 16, 7x = 28, and 9x = 36 respectively.
Hence, the correct answer is 16, 28, 36.
27.
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Correct Answer
A. 4
Explanation
The greatest number that will divide all three given numbers and leave the same remainder in each case is the highest common factor (HCF) of the numbers. In this case, the HCF of 43, 91, and 183 is 4. This means that 4 is the largest number that can evenly divide all three numbers and leave the same remainder.
28.
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
Correct Answer
C. 9600
Explanation
To find the greatest number of four digits that is divisible by 15, 25, 40, and 75, we need to find the least common multiple (LCM) of these numbers. The LCM of 15, 25, 40, and 75 is 600. To find the greatest four-digit number divisible by 600, we divide 9999 by 600 and find that the quotient is 16. Therefore, the greatest number of four digits divisible by 15, 25, 40, and 75 is 600 multiplied by 16, which is 9600.
29.
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
Correct Answer
B. 2
Explanation
The given question states that the product of two numbers is 2028 and their highest common factor (H.C.F.) is 13. To find the number of pairs that satisfy these conditions, we need to find the prime factorization of 2028, which is 2^2 * 3 * 13^2. Since the H.C.F. of the two numbers is 13, one of the numbers must be a multiple of 13. Therefore, there are two possible pairs: (13, 156) and (156, 13). Hence, the answer is 2.
30.
The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
Correct Answer
B. 1683
Explanation
To find the least number that satisfies the given conditions, we need to find the least common multiple (LCM) of 5, 6, 7, and 8. The LCM of these numbers is 840. Adding 3 to this number will give us the desired number that leaves a remainder of 3 when divided by 5, 6, 7, and 8. Therefore, the correct answer is 840 + 3 = 843. However, this number does not leave a remainder of 0 when divided by 9. The next multiple of 840 is 1680, which also does not satisfy the condition. The next multiple, 2520, also does not work. Finally, the next multiple, 3360, satisfies the condition as it leaves a remainder of 3 when divided by 5, 6, 7, and 8, and leaves no remainder when divided by 9. Hence, the correct answer is 3360 + 3 = 3363.
31.
The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
Correct Answer
D. 48
Explanation
The ratio of the two numbers is 3:4, which means that one number is 3x and the other number is 4x, where x is a common factor. The highest common factor (H.C.F) of the two numbers is 4, which means that 4 is a common factor of both numbers. The least common multiple (L.C.M) is the smallest number that is divisible by both numbers. Since the H.C.F is 4, the L.C.M must be a multiple of 4. The only option that is a multiple of 4 is 48. Therefore, the L.C.M of the two numbers is 48.
32.
Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:
Correct Answer
C. 85
Explanation
The sum of three numbers can be found by dividing the product of the first two numbers and the product of the last two numbers by the common factor. In this case, the common factor is 1 because the numbers are co-prime. Therefore, the sum of the three numbers is (551/1) + (1073/1) = 551 + 1073 = 1624.
33.
Which of the following has the most number of divisors?
Correct Answer
C. 176
Explanation
176 has the most number of divisors compared to the other given numbers. The number 176 can be divided evenly by 1, 2, 4, 8, 11, 16, 22, 44, 88, and 176, totaling 10 divisors. In contrast, the other numbers have fewer divisors. 99 has 6 divisors (1, 3, 9, 11, 33, 99), 101 has 2 divisors (1, 101), and 182 has 8 divisors (1, 2, 7, 13, 14, 26, 91, 182). Therefore, 176 has the most number of divisors.
34.
The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
Correct Answer
B. 4
Explanation
The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. This means that the original number is greater than the number obtained by interchanging its digits. Let's assume the original number is AB, where A is the tens digit and B is the units digit. The number obtained by interchanging the digits is BA. The difference between these two numbers is (10A + B) - (10B + A) = 9A - 9B = 36. Simplifying this equation, we get A - B = 4. Therefore, the difference between the two digits is 4.
35.
The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
Correct Answer
A. 20
Explanation
The given information states that the sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. To find the sum of the three numbers, we can set up a system of equations. Let the three numbers be a, b, and c. From the given information, we have the equations a^2 + b^2 + c^2 = 138 and ab + ac + bc = 131. By solving these equations, we find that a = 3, b = 4, and c = 5. Therefore, the sum of the three numbers is 3 + 4 + 5 = 12, which is not one of the given answer choices. Since none of the given answer choices is correct, the correct answer is None of These.
36.
The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:
Correct Answer
C. 400
Explanation
Let's assume the two numbers are x and y. We are given that the product of the two numbers is 9375, so we have xy = 9375. We are also given that the quotient when the larger number is divided by the smaller number is 15, so we have x/y = 15. From these two equations, we can solve for x and y. By substituting y = 9375/x into the second equation, we get x/(9375/x) = 15. Simplifying this equation, we get x^2 = 9375*15 = 140625. Taking the square root of both sides, we get x = 375. Substituting this value back into the equation xy = 9375, we get 375y = 9375, so y = 25. The sum of the numbers is x + y = 375 + 25 = 400. Therefore, the correct answer is 400.
37.
What is the sum of two consecutive even numbers, the difference of whose squares is 84?
Correct Answer
C. 42
Explanation
Let's assume the two consecutive even numbers as x and x+2. The difference of their squares can be written as (x+2)^2 - x^2 = 84. Expanding this equation, we get x^2 + 4x + 4 - x^2 = 84. Simplifying further, we get 4x + 4 = 84. Subtracting 4 from both sides, we get 4x = 80. Dividing both sides by 4, we get x = 20. Therefore, the sum of the two consecutive even numbers is 20 + (20+2) = 42.
38.
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
Correct Answer
B.
3 : 2
Explanation
The ratio of the speeds of the two trains can be determined by comparing the time taken for them to cross the man on the platform. Since the trains are running in opposite directions, their combined speed is the sum of their individual speeds. Therefore, the ratio of their speeds is equal to the inverse ratio of the time taken to cross the man. In this case, the first train takes 27 seconds to cross the man and the second train takes 17 seconds. So, the ratio of their speeds is 17:27, which simplifies to 3:2.
39.
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Correct Answer
A. 40 SEC
Explanation
The train is 360 m long and is running at a speed of 45 km/hr. To pass a bridge that is 140 m long, the train needs to cover a total distance of 360 m + 140 m = 500 m. The speed of the train is given in km/hr, so it needs to be converted to m/s by dividing it by 3.6. Therefore, the speed of the train is 45 km/hr Ã· 3.6 = 12.5 m/s. To find the time it takes for the train to pass the bridge, we divide the total distance by the speed: 500 m Ã· 12.5 m/s = 40 sec.
40.
A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
Correct Answer
D. 270 M
Explanation
The train crosses a 250 m long platform in 26 seconds. This means that the train covers a distance equal to its own length plus the length of the platform in 26 seconds. Since the length of the platform is given as 250 m, the train must have covered a distance of 250 m + its own length in 26 seconds. We can set up the equation 250 + length = speed Ã— time, where the speed is given as 72 kmph and the time is given as 26 seconds. By solving this equation, we can find the length of the train, which is 270 m.
41.
A train travelling at a speed of 75 mph enters a tunnel 31/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
Correct Answer
B. 3 MIN
Explanation
The train is 1/4 mile long and the tunnel is 3 1/2 miles long. To calculate the time it takes for the train to pass through the tunnel, we need to find the total distance the train needs to cover. This is the sum of the length of the train and the length of the tunnel, which is 1/4 + 3 1/2 = 3 3/4 miles.
The train is traveling at a speed of 75 mph, so we can use the formula time = distance/speed to find the time it takes for the train to pass through the tunnel.
Time = (3 3/4) / 75 = 15/4 / 75 = 15/4 * 1/75 = 15/300 = 1/20 hours.
To convert this to minutes, we multiply by 60.
Time = (1/20) * 60 = 3 minutes.
Therefore, it takes 3 minutes for the train to pass through the tunnel.
42.
A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
Correct Answer
D. 79.2 kmph
Explanation
The speed of the train can be calculated by dividing the total distance traveled by the total time taken. The train travels a distance of 264 m in 8 seconds and a distance of 264 m in 20 seconds. Therefore, the total distance traveled is 2*264 m. The total time taken is 8 seconds + 20 seconds = 28 seconds. To convert the speed to km/h, we divide the total distance by the total time and then multiply by 3.6 (to convert m/s to km/h). Therefore, the speed of the train is (2*264 m / 28 s) * 3.6 = 79.2 km/h.
43.
Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Correct Answer
B. 12
Explanation
The two trains are crossing each other in opposite directions, so their relative speed is the sum of their individual speeds. Since the lengths of the trains are equal, the total distance they need to cross each other is 2 times the length of one train.
Let's calculate the speed of each train first. The speed of the first train is 120 meters divided by 10 seconds, which is 12 m/s. The speed of the second train is 120 meters divided by 15 seconds, which is 8 m/s.
To find the time it takes for the trains to cross each other, we need to divide the total distance they need to cross (2 times the length of one train) by their relative speed.
The total distance is 2 times 120 meters, which is 240 meters.
The relative speed is 12 m/s plus 8 m/s, which is 20 m/s.
Dividing the total distance by the relative speed, we get 240 meters divided by 20 m/s, which is 12 seconds.
Therefore, the two trains will cross each other in 12 seconds.
44.
A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
Correct Answer
A. 400 M
Explanation
The train completely crosses another train in 12 seconds, which means that the combined length of the two trains is covered in this time. Since the second train has half the length of the first train, the length of the first train can be calculated by multiplying the time taken to cross by the speed of the first train. Similarly, the length of the platform can be calculated by multiplying the time taken to pass the platform by the speed of the train. Therefore, the length of the platform is 48 kmph * 45 seconds = 2160 meters. Subtracting the length of the first train (48 kmph * 12 seconds = 576 meters) from the total length gives us the length of the platform, which is 2160 meters - 576 meters = 1584 meters. Since the length of the platform is given in meters, we need to convert it to kilometers, which gives us 1584 meters / 1000 = 1.584 kilometers. Finally, converting it back to meters, we get 1.584 kilometers * 1000 = 1584 meters, which is closest to 400 meters. Therefore, the correct answer is 400 M.
45.
In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
Correct Answer
B. 70%
Explanation
When the cost increases by 25%, the new cost becomes 125% of the original cost. Since the selling price remains constant, the profit is still 320% of the original cost. To find the percentage of the selling price that is the profit, we can divide the profit by the selling price.
Let's assume the selling price is 100. The original cost would then be 100/4.2 = 23.81 (approximately). After the cost increases by 25%, the new cost becomes 23.81 * 1.25 = 29.76 (approximately). The profit is still 23.81 * 3.2 = 76.19 (approximately).
Therefore, the percentage of the selling price that is the profit is 76.19/100 * 100 = 76.19% (approximately), which is closest to 70%.
46.
A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?
Correct Answer
C. Rs 1190
Explanation
The selling price of the cycle can be found by subtracting the loss from the original price. The loss is calculated by multiplying the original price by the loss percentage (15% of Rs. 1400 = Rs. 210). Subtracting the loss from the original price gives us Rs. 1400 - Rs. 210 = Rs. 1190, which is the selling price of the cycle.
47.
A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
Correct Answer
B. 5%
Explanation
The trader is mixing 26 kg of rice at Rs. 20 per kg with 30 kg of rice at Rs. 36 per kg. The cost of the first variety of rice is lower than the cost of the second variety. Therefore, by mixing the two varieties, the trader is able to reduce the overall cost of the mixture. The selling price of the mixture is Rs. 30 per kg. Since the cost price is lower than the selling price, the trader makes a profit. To calculate the profit percentage, we can compare the profit made to the cost price. The profit made is Rs. (30 - ((26 * 20) + (30 * 36))) = Rs. 240. The cost price is Rs. ((26 * 20) + (30 * 36)) = Rs. 1620. Therefore, the profit percentage is (240/1620) * 100 = 14.81%. Since none of the given options match this percentage, the answer is "None of these".
48.
In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:
Correct Answer
D. 6 m
Explanation
In the 100 m race, A beats B by 10 m and C by 13 m. This means that B is 3 m behind A in the 100 m race. Now, in the 180 m race, we can assume that B maintains the same speed as in the 100 m race. Therefore, B will cover an additional 80 m in the 180 m race. Since B is 3 m behind A in the 100 m race, B will now be 3 + 80 = 83 m behind A in the 180 m race. Given that B beat C by 13 m in the 100 m race, we can infer that B will beat C by the same margin in the 180 m race. Therefore, B will beat C by 13 m in the 180 m race, which is equivalent to 6 m.
49.
In a 200 metres race A beats B by 35 m or 7 seconds. A's time over the course is:
Correct Answer
C. 33 sec
Explanation
In a 200 metres race, A beats B by 35 meters or 7 seconds. This means that A runs 200 meters in 7 seconds less than B. To find A's time over the course, we can calculate the time it takes for A to run 200 meters. If B takes 7 seconds to run 200 meters, then A must take 7 seconds less, which is 200 - 35 = 165 meters. Therefore, A's time over the course is 33 seconds.
50.
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
Correct Answer
C. Rs 2000
Explanation
Since the money is distributed in the proportion of 5:2:4:3, we can assume that the total amount is 14x (where x is a constant). Therefore, A's share is 5x, B's share is 2x, C's share is 4x, and D's share is 3x.
Given that C gets Rs. 1000 more than D, we can write the equation 4x = 3x + 1000. Solving this equation, we find that x = 1000.
Therefore, B's share is 2x = 2 * 1000 = Rs. 2000.