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1. Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
2. Find the average of the first 20 natural numbers?
3. Two-fifth of one-third of three-seventh of a number is 15. What is 40% of that number?
4. The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
5. 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:
6. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
7. The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is?
8. What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?
9. Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
10. If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest?
11. A certain number when divided by 45 leaves a remainder 31, what is the remainder if the same number be divided by 15?
12. 96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
13. A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
14. The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
15. What should be the least number to be added to the 51234 number to make it divisible by 9?
16. A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
17. Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer)
18. 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Men’s wages are?
19. A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
20. In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case?
21. A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
22. Three numbers are in the ratio 3:4:5 and their L.C.M is 2400. Their H.C.F is:
23. 7589 - ? = 3434
24. What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?
25. The C.I. on a certain sum for 2 years Rs.41 and the simple interest is Rs.40. What is the rate percent?
26. If (4^{61} + 4^{62} + 4^{63} + 4^{64}) is divisible by ?, then ? =
27. The product of two successive numbers is 4556. Which of the following is the larger of the two numbers?
28. A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in?
29. The average of 35 numbers is 25. If each number is multiplied by 5, find the new average?
30. Find the one which does not belong to that group ?
31. The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?
32. A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old id the mother at present?
33. Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?
34. 10 books are placed at random in a shelf. The probability that a pair of books will always be together is -.
35. 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?
36. A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
37. A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
38. The difference between a number and its two-fifth is 510. What is 10% of that number?
39. The G.C.D of 1.08, 0.36 and 0.9 is
40. (17^{14} * 17^{16}) / 17^{-8} = ?
41. The areas of the two spheres are in the ratio 1: 4. The ratio of their volume is?
42. A batsman in his 17^{th} innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17^{th}innings?
43. A man gets a simple interest of Rs.500 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate.
44. If three eighth of a number is 141. What will be the approximately value of 32.08% of this number?
45. In how many years does a sum of Rs. 5000 yield a simple interest of Rs. 16500 at 15% p.a.?
46. A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
47. There are some rabbits and peacocks in a zoo. The total number of their heads is 60 and total number of their legs is 192. Find the number of total rabbits?
48. I. a^{2} + 8a + 16 = 0, II. b^{2} - 4b + 3 = 0 to solve both the equations to find the values of a and b?
49. Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
50. A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left?