Mains Level Mathematics Enter email to receive results: 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?1/31/41/61/8 2. The product of 2 numbers is 1575 and their quotient is 9/7. Then the sum of the numbers is 74 78 80 90 3. The value of (81)3.6 * (9)2.7/ (81)4.2 * (3) is 3698.2 4. √6+√6+√6+… is equal to2543 5. The sum of the squares of two natural consecutive odd numbers is 394. The sum of the numbers is24 324028 6. When (6767 +67) is divided by 68, the remainder is- 1 63 66 67 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 then4b-a2 /a =3 4b-2a /a2 =2(a+1)2 = 4b A(a+2)/b = 4 8. If 738 A6A is divisible by 11, then the value of A is6391 9. The east positive integer that should be subtracted from 3011 x 3012 so that the difference is perfect square is-300930103011 3012 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-2850375027501000 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?15 2018 30 12. 11. The square root of (0.75)3 /1-0.75 + [0.75 + 90.75)2 +1] is-1234 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 :4320432004320004320000 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:25:2828:2522:2525:22 15. If p=99, the value of p(p² + 3p + 3) is:999999998999998998990000 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 :12131415 17. 70% of the cost price of a equal to the 40% of its selling price. What is the profit or loss percentage ?70758085 18. Find the least number which when divided by 12, 18 ,36 and 45 leaves the remainder 8,14,32 and 41 respectively174175176178 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)120180200240 20. If a sum of Rs.12500 is invested for 1 year at 12% per annum interest being compounded semiannually, then interest earned is1200140015451600 21. is divisible by:124125126127 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)35363839 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 is31172026 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.33,5560,6915,2836,115 25. Find the sum of all prime numbers between 10 and 909441064774844 26. Simplify:- 18800 / 470 / 201234 27. Find the sum of first 30 natural numbers470468465463 28. Average of 10 numbers is zero. At most how many numbers may be greater than zero0159 29. Find the average of all numbers between 6 and 34 which are divisible by 515202530 30. Find the HCF of22×32×72,2×34×7128126146434 31. HCF of22×32×52,24×34×53×1122×32×52,24×34×53×11 is2^4×3^4×5^32^4×3^4×5^3×112^2×3^2×5^22×3×5 32. What will be the LCM of 8, 24, 36 and 5454108216432 33. Find the HCF of2/3,4/6,8/272/278/32/38/27 34. Raju age after 15 years will be 5 times his age 5 years back, What is the present age of Raju1514108 35. Ages of two persons differ by 16 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age12,2814,3016,3218,34 36. Ten years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages35344525 37. Sachin was twice as old as Ajay 10 years back. How old is Ajay today if Sachin will be 40 years old 10 years hence18251520 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 ages30353741 39. (10)^150÷(10)^14610100100010000 40. if 6^m=46656, What is the value of 6^m−27776778212961290 41. (25)^7.5×(5)^2.5÷(125)^1.5=5^?9.711.51213 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? 45303540 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 is30°40°45°60° 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?23 years22 years21 years20 years 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?24222628 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?10978 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?50 years40 years 60 years 30 years 48. If a certain sum of money can become 5 times of its principal in 10 years, then the rate of interest is20%30%40%50% 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 is30°40°45°60° 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?25% 20%40%30% 51. A fruit vendor gives 2 successive discounts of 10% and 14%. What is the overall discount given?22.422.622.722.8 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?12000130001400015000 53. Six friends have an average height of 167 cm. Rahul with height 162 cm leaves. What is the new average height?166168169170 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?1225142515251625 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?16.67171818.78 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…..80818286 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…..233.54 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…22.12.22.4 59. A sum of money doubles itself at compound interest in 15 years. In how many years it will become eight times?40454850 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?1260128013001350 61. If the diameter of a sphere is 14 cm, then what is the surface area (in cm^{2}) of the sphere?616618619621 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?92500955009750099000 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?400600800900 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?16202224 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?1234 66. After deducting 60% from a certain number and then deducting 15% from the remainder, 1428 is left. What was the initial number?4200430044004500 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?130132134134.4 68. A certain sum of money triples itself in 5 years at simple interest. In how many years it will be five times?581012 69. If x + (1/x) = 2, then what is the value of x^{64} + x^{121}?0123 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)?0123 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-7000800090009500 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-2:33:21:22:1 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-7.12 p.m7.14p.m7.16p.m7.18 p.m 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?78910 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-300310312313 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-30323436 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 –1616-1/316-2/317 78. 17, 19, 23, 29,(…..),37383940 79. 11, 12, 17, 18, 23, 24,(…..)29303132 80. 134, 245, 356, 467, (….)478578580612 81. If a whole number n is divided by 4, we will get 3 as remainder. What will be the remainder if 2n is divided by 4 ?1234 82. If the number 481*673 is completely divisible by 9, what is the the smallest whole number in place of *?6789 83. How many of the following numbers are divisible by 132 ? 264, 396, 462, 792, 968, 2178, 5184, 63364567 84. A number when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 31?4567 85. The number 1242*2 is completely divisible by 3. What is the smallest number in place of * ?0123 86. Sumitra has an average of 56% on her first 7 examinations. How much she should make on her eighth examination to obtain an average of 60% on 8 examinations?6868788898 87. The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.4848.554950 88. In a school with 600 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average of the school is 11 years 9 months, then the number of girls in the school is: ?150200250300 89. If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is:5454.685555.25 90. If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?5:34:55:66:7 91. If Rs. 782 be divided into three parts, proportional to : : , then the first part is:182200204205 92. Three containers have their volumes in the raito 3 : 4 : 5, They are full of mixtures of milk and water. The mixtures contain milk and water in the ratio of (4 : 1), (3 : 1) and (5 : 2) respectively. The contents of all these three containers are poured into a fourth container. The ratio of milk and water in the fourth container is :157:5353:55155:56None of these 93. Two number 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:27303334 94. 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?500150020002200 95. In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?50100150200 96. If 3^{(x – y)} = 27 and 3^{(x + y)} = 243, then x is equal to:3456 97. (17)^{3.5} x (17)^{?} = 17^{8}33.544.5 98. The value of [(10)_{150} ÷(10)_{146}] is1000100001000001000000 99. (0.04)^{-1.5} = ?100125150155 100. If 2x = 3√32, then x is equal to3/55/31520 Loading...