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1. Surface area of two spheres are in the ratio 1:4 what is the ratio of their volumes?
2. Find the numbers which are in the ratio 3 : 2 : 4 such that the sum of the first and the second added to the difference of the third and the second is 21 ?
3. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
4. A tap can fill a tank in 6 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?
5. Which one of the following is the least number of four digits divisible by 71?
6. Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
7. The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above conditions is:
8. How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?
9. Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 8160, how much money did he borrow?
10. A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
11. A building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is?
12. An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point?
13. A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?
14. A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
15. The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is?
16. 85% of a number is added to 24, the result is the same number. Find the number?
17. An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
18. If the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is?
19. The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?
20. One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number?
21. Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 30% profit?
22. Find the smallest four-digit number which is a multiple of 112.
23. 7394 - 1236 - 4652 = ?
24. A train 100 m long crosses a platform 125 m long in 15 sec; find the speed of the train?
25. Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?
26. Mudit's age 18 years hence will be thrice his age four years ago. Find Mudit's present age?
27. The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
28. Excluding stoppages, the speed of a bus is 54 km/hr and including stoppages, it is 45 km/hr. For how many minutes does the bus stop per hour?
29. 12 3/4 * (1 2/17 / 8 1/6) / 5 4/3 = ?
30. The sum of four consecutive even numbers is 36. Find the sum of the squares of these numbers?
31. Find the average of the first 20 natural numbers?
32. Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
33. 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?
34. 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 meet again at the starting point?
35. Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
36. The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is:
37. Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 3 minutes A is turned off. After how much more time will the cistern be filled?
38. A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in?
39. Find the one which does not belong to that group ?
40. What percent of 120 are 90?
41. The C.I. on a certain sum for 2 years Rs.41 and the simple interest is Rs.40. What is the rate percent?
42.
The sub-duplicate ratio of 1:4 is
43. A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?
44. Two numbers are in the ratio 3:5. If 9 is subtracted from each, the new numbers are in the ratio 12:23. The smaller number is:
45. A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
46. If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is:
47. Simplify : (y^{4b-a} . y^{4c-b} . y^{4a-c}) / (y^{a} . y^{b} . y^{c})^{3}
48. The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
49. The simple interest on Rs.12000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for five years at the same rate of interest.
50. 8 2/3 + 6 4/5 = ?