# Mains Level Mathematics

1. Three people who work full-time are to work together on a project, but their total time on the project is to be equivalent to that of only one person working full-time. If one of the people is budgeted for 1/2 of his time to the project and a second person for 1/3 of her time, what part of the third worker's time should be budgeted to this project?
2. The product of 2 numbers is 1575 and their quotient is 9/7. Then the sum of the numbers is
3. The value of (81)3.6 * (9)2.7/ (81)4.2 * (3) is
4. √6+√6+√6+… is equal to
5. The sum of the squares of two natural consecutive odd numbers is 394. The sum of the numbers is
6. When (6767 +67) is divided by 68, the remainder is-
7. In a division sum, the divisor is 4 times the quotient and twice the remainder. If a and b are respectively the divisor and the dividend then
8. If 738 A6A is divisible by 11, then the value of A is
9. The east positive integer that should be subtracted from 3011 x 3012 so that the difference is perfect square is-
10. P, Q, R are employed to do a work for Rs. 5750. P and Q together finished 19/23 of work and Q and R together finished 8/23 of work. Wage of Q, in rupees, is-
11. A can do a piece of work in 24 day, B in 32 days and C in 64 days. All begin to do it together, but A leaves after 6 days and B leaves 6 days before the completion of the work. How many days did the work last?
12. 11.  The square root of (0.75)3 /1-0.75 + [0.75 + 90.75)2 +1] is-
13. A tap drips at a rate of one drop/sec. 600 drops make 100 ml. The number of liters wasted in 300 days is :
14. A policeman starts to chase a thief. When the thief goes 10 steps the policeman moves 8 steps. 5 steps of the policeman is equal to 7 steps of the thief. The ratio of the speeds of the policeman and the thief is:
15. If p=99, the value of p(p² + 3p + 3) is:
16. If a person travel from a point L towards east for 12 km and then travel 5 km toward north and reaches a point M, then shortest distance from L to M is :
17. 70% of the cost price of a equal to the 40% of its selling price. What is the profit or loss percentage ?
18. Find the least number which when divided by 12, 18 ,36 and 45 leaves the remainder 8,14,32 and 41 respectively
19. A motor cycle gives an average of 45 km per litre. If the cost of petrol is Rs.20 per litre. The amount required to complete a journey of 540 km is, (in rupees)
20. If a sum of Rs.12500 is invested for 1 year at 12% per annum interest being compounded semiannually, then interest earned is
21. is divisible by:
22. The average age of eight teachers in a school is 40 years. A teacher among them died at the age of 55 years whereas another teacher whose age was 39 years joins them. The average age of the teachers in the school now is (in years)
23.

The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight (in kg) of B is
24. Two numbers are in the ratio of 3: 5. If 9 be subtracted from each, then they are in the ratio of 12: 23. Find the numbers.
25. Find the sum of all prime numbers between 10 and 90
26. Simplify:-

27.

28.

29.

30.

22×32×72,2×34×7
31.

#### HCF of

22×32×52,24×34×53×1122×32×52,24×34×53×11 is
32.

33.

2/3,4/6,8/27
34.

35.

36.

37.

38.

#### Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages

39. (10)^150÷(10)^146
40. if 6^m=46656, What is the value of 6^m2
41. (25)^7.5×(5)^2.5÷(125)^1.5=5^?
42. Ten years ago, P was half of Q's age. If the ratio of their present ages is 3:4, what will be the total of their present ages?
43. Consider ΔABD such that angle ADB = 20° and C is a point on BD such that AB=AC and CD=CA. Then the measure of angle ABC is
44. A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
45. Present ages of Kiran and Syam are in the ratio 5:4. Three years hence, the ratio of their ages will become 11:9. What is Syam's present age in years?
46. A is two years older than B who is twice as old as C. The total of the ages of A, B and C is 27. How old is B?
47. After six years, Sandeep's age will be three-seventh of his father's age. Ten years ago the ratio of their ages was 1:5. What is Sandeep's father's age at present?
48. If a certain sum of money can become 5 times of its principal in 10 years, then the rate of interest is
49. Consider ΔABD such that angle ADB = 20° and C is a point on BD such that AB=AC and CD=CA. Then the measure of angle ABC is
50. An amount of Rs. 10,000 becomes Rs. 20,736 in 2 years. If the rate of interest is compounded half yearly, what is the annual rate of interest?
51. A fruit vendor gives 2 successive discounts of 10% and 14%. What is the overall discount given?
52. The total sales of a company amounts to Rs. 24 crores and the volume sold is 20000 units. What is the average price/unit?
53. Six friends have an average height of 167 cm. Rahul with height 162 cm leaves. What is the new average height?
54. Average production of a farm was 1500 tons in the months Jan-March. If April with 1200 tones is included. What will be the new average from Jan-April?
55. Sheila purchase 20 kg apples at Rs. 15 kg and another 10 kg apples at Rs. 20 kg. What is the average cost/kg?
56. 1 kg of tea and 1 kg of sugar together cost Rs. 95. If the price of tea falls by 10% and that of sugar rises by 20% the price of 1 kg each, combined comes to Rs. 90. The original price of tea in Rs. Per kg is…..
57. Madhu got married 6 years ago. Today her age is 1 ¼ times her age at the time of marriage. Her son’s age is 1/10 her age. Her son’s age is…..
58. In a village the current birth rate per thousand is 55 whereas corresponding death rate is 34 per thousand. The net growth rate in term of population increase will be…
59. A sum of money doubles itself at compound interest in 15 years. In how many years it will become eight times?
60. Raman can do a work in 5 days, Jatin can do the same work in 7 days and Sachin can do the same work in 9 days. If they do the same work together and they are paid Rs 2860, then what is the share (in Rs) of Raman?
61. If the diameter of a sphere is 14 cm, then what is the surface area (in cm2) of the sphere?
62. After two successive discounts of 20% and 35%, an article is sold for Rs 50700. What is the marked price (in Rs) of the article?
63. Rs 3200 is divided among A, B and C in the ratio of 3 : 5 : 8 respectively. What is the difference (in Rs) between the share of B and C?
64. The average of 5 members of a family is 24 years. If the youngest member is 8 years old, then what was the average age (in years) of the family at the time of the birth of the youngest member?
65. If the price of pen decreases by 20%, then a man can buy 10 more pens for Rs 100. What is the new price (in Rs) of each pen?
66. After deducting 60% from a certain number and then deducting 15% from the remainder, 1428 is left. What was the initial number?
67. A train travels 40% faster than a car. Both start from point A at the same time and reach point B, 140 km away at the same time. On the way the train takes 25 minutes for stopping at the stations. What is the speed (in km/hr) of the train?
68. A certain sum of money triples itself in 5 years at simple interest. In how many years it will be five times?
69. If x + (1/x) = 2, then what is the value of x64 + x121?
70. If a + b + c = 27, then what is the value of (a – 7)3 + (b – 9)3 + (c – 11)3 – 3(a – 7)(b – 9)(c – 11)?
71. A and B earn in the ratio 2:1. They spend in the ratio 5:3 and save in the ratio 4:1. If the total monthly savings of both A and B are Rs.5,000, the monthly income of B is-
72. The ratio of the sum of two numbers and their difference is 5:1. The ratio of the greater number to the smaller number is-
73. A cistern has 3 pipes A, B and C. A and B can fill it in 3 and 4 hours respectively, and C can empty it in 1 hour. If the pipes are opened at 3 p.m., 4 p.m. and 5 p.m. respectively on the same day, the cistern will be empty at-
74. If A works alone, he would take 4 days more to complete the job than if both A and B worked together. If B worked alone, he would take 16 days more to complete the job than if A and B work together. How many days would they take to complete the work if both of them worked together?
75. 250 men can finish a work in 20 days working 5 hours a day. To finish the work within 10 days working 8 hours a day, the minimum number of men required is-
76. 2 men and 5 women can do a work in 12 days. 5 men 2 women can do that work in 9 days. Only 3 women can finish the same work in-
77. While selling, a businessman allows 40% discount on the marked price and there is a loss of 30%. If it is sold at the marked price, profit per cent will be –
78.
79.
80.
81.

82.

83.

#### How many of the following numbers are divisible by 132 ?

264, 396, 462, 792, 968, 2178, 5184, 6336
84.

85.

86.

87.

88.

89.

90.

91.

92.

93.

94.

95.

96.

97.

98.

99.

100.