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1. A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
2. Mudit's age 18 years hence will be thrice his age four years ago. Find Mudit's present age?
3. What is the difference between the largest number and the least number written with the figures 3, 4, 7, 0, 3?
4. Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?
5. 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?
6. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
7. (27^{2/3} * 9^{1/2} * 81^{1/4})^{-1/4} = ?
8. I. a^{2} - 13a + 42 = 0, II. b^{2} - 15b + 56 = 0 to solve both the equations to find the values of a and b?
9. 2/3 * 5 1/2 * 2 * 7 5/6 * 9/11 = ?
10. Two pipes A and B can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
11. What percent of 125 is 16?
12. What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
13. Income and expenditure of a person are in the ratio 5:4. If the income of the person is Rs.18000, then find his savings?
14. Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40:57. What is Sumit's present salary?
15. A number consists of two digits. If 3/5 of 1/5 of the number is 9. Find the sum of its two digits?
16. The sector of a circle has radius of 21 cm and central angle 135^{o}. Find its perimeter?
17. A sum of money invested at C.I. amounts to Rs. 800 in 3 years to Rs. 840 in 4 years. The rate of interest per annum is?
18. 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.
19. A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag?
20. The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is:
21. Find the one which does not belong to that group ?
22. The tens digit of a two-digit number is two more than its unit digit. The two-digit number is 7 times the sum of the digits. Find the units digits?
23. Five bells first begin to toll together and then at intervals of 5, 10, 15, 20 and 25 seconds respectively. After what interval of time will they toll again together?
24. A property decreases in value every year at the rate of 6 1/4% of its value at the beginning of the year its value at the end of 3 years was Rs.21093. Find its value at the beginning of the first year?
25. A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.
26. The sum of the present ages of 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:
27. A certain number of men can do a work in 65 days working 6 hours a day. If the number of men are decreased by one-fourth, then for how many hours per day should they work in order to complete the work in 40 days?
28. The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4?
29. The area of the cardboard(in cm^{2}) needed to make a box of size 25 cm * 15 cm * 8 cm will be?
30. Find the number of factors of 300 excluding 1 and itself.
31. A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
32. The product of two numbers is 4107. If the H.C.F of these numbers is 37, then the greater number is:
33. Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder?
34. The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
35. An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?
36. The simple form of the ratio 2/3:2/5 is?
37. Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
38. If a and b are the roots of the equation x^{2} - 9x + 20 = 0, find the value of a^{2} + b^{2} + ab?
39. A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
40. If the roots of the equation 2x^{2} - 5x + b = 0 are in the ratio of 2:3, then find the value of b?
41. Find the one which does not belong to that group ?
42. Rs.525 among A, B and C such that B may get 2/3 of A and C together get. Find the share of C?
43. A bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 2:3:4. If the total value of all the coins in the bag is Rs.400, find the number of coins of each kind?
44. The average marks in mathematics scored by the pupils of a school at the public examination were 39. If four of these pupils who actually scored 5, 12, 15 and 19 marks at the examination had not been sent up, the average marks for the school would have been 44. Find the number of pupils sent up for examination from the school?
45. The price of a T.V. set worth Rs. 20000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
46. A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
47. Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?
48. There are two numbers. If 40% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
49. A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18000. A's share is?
50. A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the room?