Quantitative Aptitude is a crucial scoring section in Staff Selection Commission (SSC) exams such as the CGL, CHSL, CPO, and MTS. The syllabus typically encompasses elementary mathematics up to the 10th-grade standard, broadly divided into Arithmetic and Advanced Mathematics. Arithmetic focuses on foundational topics like percentages, ratio and proportion, time and work, and profit and loss, which test real-world problem-solving skills. Advanced Math, which carries significant weightage in exams like the CGL, evaluates skills in algebra, geometry, trigonometry, and mensuration. Mastering this section requires not only strict conceptual clarity but also the ability to apply shortcut techniques for rapid calculation within tight time limits.
1. What is the unit digit of 7^105?
Correct Answer: c) 7
Explanation:
The cyclicity of the unit digit of 7 is 4 (7, 9, 3, 1). Dividing 105 by 4 gives a remainder of 1. Therefore, the unit digit is the same as 7^1, which is 7.
2. What is the sum of the first 50 natural numbers?
Correct Answer: b) 1275
Explanation:
The sum of the first n natural numbers is given by n(n+1)/2. For n=50, the sum is (50 * 51) / 2 = 1275.
3. Find the HCF of 2/3, 4/5, and 6/7.
Correct Answer: a) 2/105
Explanation:
The HCF of fractions is (HCF of Numerators) / (LCM of Denominators). HCF(2, 4, 6) = 2. LCM(3, 5, 7) = 105. Thus, HCF is 2/105.
4. What is the LCM of 3, 4, 5, and 6?
Correct Answer: b) 60
Explanation:
The lowest common multiple (LCM) of 3, 4, 5, and 6 is the smallest number divisible by all, which is 60.
5. Find the largest 4-digit number exactly divisible by 12, 15, 18, and 27.
Correct Answer: a) 9720
Explanation:
LCM of 12, 15, 18, 27 is 540. The largest 4-digit number is 9999. Dividing 9999 by 540 leaves a remainder of 279. Subtracting 279 from 9999 gives 9720.
6. What is the value of sqrt(6 + sqrt(6 + sqrt(6 + ...))) to infinity?
Correct Answer: b) 3
Explanation:
Let x = sqrt(6 + x). Squaring both sides gives x^2 - x - 6 = 0, which factors to (x-3)(x+2) = 0. Since x must be positive, x = 3.
7. Find the sum of 1/2 + 1/6 + 1/12 + ... + 1/90.
Correct Answer: b) 9/10
Explanation:
This can be written as (1 - 1/2) + (1/2 - 1/3) + ... + (1/9 - 1/10). All intermediate terms cancel out, leaving 1 - 1/10 = 9/10.
8. Find the remainder when 17^200 is divided by 18.
Correct Answer: a) 1
Explanation:
Using the remainder theorem, 17 divided by 18 gives a remainder of -1. So, (-1)^200 = 1. The remainder is 1.
9. Find the difference between the local (place) value and face value of 7 in the numeral 32675149.
Correct Answer: c) 69993
Explanation:
The place value of 7 is 70,000 and its face value is 7. Difference = 70000 - 7 = 69993.
10. A number when divided by 899 gives a remainder of 63. What will be the remainder if the same number is divided by 29?
Correct Answer: b) 5
Explanation:
Since 899 is perfectly divisible by 29, the remainder when the number is divided by 29 will be the remainder of 63 divided by 29, which is 5.
11. If x + (1/x) = 4, find the value of x^2 + (1/x^2).
Correct Answer: a) 14
Explanation:
Squaring both sides: x^2 + (1/x^2) + 2(x)(1/x) = 16. So, x^2 + (1/x^2) = 16 - 2 = 14.
12. If x + (1/x) = 3, find the value of x^3 + (1/x^3).
Correct Answer: a) 18
Explanation:
Using the formula (a+b)^3, x^3 + (1/x^3) = (x + 1/x)^3 - 3(x + 1/x) = 3^3 - 3(3) = 27 - 9 = 18.
13. If a + b + c = 0, find the value of a^3 + b^3 + c^3.
Correct Answer: b) 3abc
Explanation:
According to the algebraic identity, if a + b + c = 0, then a^3 + b^3 + c^3 = 3abc.
14. What are the roots of the quadratic equation x^2 - 5x + 6 = 0?
Correct Answer: a) 2 and 3
Explanation:
Factoring the equation gives (x - 2)(x - 3) = 0, so the roots are x = 2 and x = 3.
15. If x - y = 4 and xy = 21, find the value of x^3 - y^3.
Correct Answer: a) 316
Explanation:
Using the identity x^3 - y^3 = (x - y)^3 + 3xy(x - y), we get 4^3 + 3(21)(4) = 64 + 252 = 316.
16. If a + b = 5 and a - b = 3, find the value of a^2 + b^2.
Correct Answer: a) 17
Explanation:
Adding equations yields 2a = 8, so a = 4. Then b = 1. Therefore, a^2 + b^2 = 16 + 1 = 17.
17. If x^4 + (1/x^4) = 119, find the value of x - (1/x).
Correct Answer: a) 3
Explanation:
Add 2 to both sides: (x^2 + 1/x^2)^2 = 121 -> x^2 + 1/x^2 = 11. Subtract 2 from both sides: (x - 1/x)^2 = 9 -> x - 1/x = 3.
18. If a + b = 10 and ab = 24, find the value of a^3 + b^3.
Correct Answer: a) 280
Explanation:
a^3 + b^3 = (a+b)^3 - 3ab(a+b) = 10^3 - 3(24)(10) = 1000 - 720 = 280.
19. Solve for x and y: 3x + 2y = 12 and 4x - y = 5.
Correct Answer: a) (2, 3)
Explanation:
Multiply the second equation by 2: 8x - 2y = 10. Add to the first: 11x = 22 -> x = 2. Substituting x=2 in 4x-y=5 gives 8-y=5 -> y=3.
20. Evaluate (x^a/x^b)^(a+b) * (x^b/x^c)^(b+c) * (x^c/x^a)^(c+a).
Correct Answer: b) 1
Explanation:
The terms simplify to x^((a-b)(a+b)) * x^((b-c)(b+c)) * x^((c-a)(c+a)) = x^(a^2-b^2 + b^2-c^2 + c^2-a^2) = x^0 = 1.
21. If A's salary is 20% more than B's, by what percent is B's salary less than A's?
Correct Answer: a) 16.66%
Explanation:
Required percentage = (20 / (100 + 20)) * 100 = (20/120)*100 = 100/6 = 16.66%.
22. The population of a town is 10000. It increases by 10% annually. What will it be after 2 years?
Correct Answer: b) 12100
Explanation:
Population after 2 years = 10000 * (1 + 10/100)^2 = 10000 * 1.1 * 1.1 = 12100.
23. The price of sugar rises by 25%. By what percent should a family decrease its consumption so that the expenditure remains the same?
Correct Answer: a) 20%
Explanation:
Percentage decrease = (25 / (100 + 25)) * 100 = (25/125)*100 = 20%.
24. A student scored 30% marks and failed by 15 marks. Another student scored 40% and got 35 marks more than the passing marks. Find the passing marks.
Correct Answer: b) 165
Explanation:
Let total marks be x. 40% of x - 30% of x = 35 + 15 -> 10% of x = 50 -> x = 500. Passing marks = 30% of 500 + 15 = 150 + 15 = 165.
25. In an election between two candidates, the winner got 60% of the total valid votes and won by 400 votes. What is the total number of votes?
Correct Answer: b) 2000
Explanation:
The winner got 60%, so the loser got 40%. The difference is 20%. Let total votes be x. 20% of x = 400 -> x = 2000.
26. If 20% of a number is 120, what will 120% of that number be?
Correct Answer: a) 720
Explanation:
Since 20% is 120, 1% is 6. Therefore, 120% is 120 * 6 = 720.
27. A man spends 70% of his income. His income increases by 20% and his expenditure increases by 10%. By what percentage do his savings increase?
Correct Answer: a) 43.33%
Explanation:
Let income = 100, exp = 70, savings = 30. New income = 120, new exp = 77, new savings = 43. Increase in savings = 13. % increase = (13/30)*100 = 43.33%.
28. Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg of fresh fruit?
Correct Answer: b) 40kg
Explanation:
The mass of pulp remains constant. Pulp in fresh fruit = 32% of 100kg = 32kg. Let dry fruit be x kg. Pulp in dry fruit = 80% of x = 32kg. So x = 32 / 0.8 = 40kg.
29. The passing percentage in an exam is 35%. A boy gets 200 marks and fails by 10 marks. What are the maximum marks?
Correct Answer: a) 600
Explanation:
Passing marks = 200 + 10 = 210. 35% of total marks = 210 -> Total marks = (210 / 35) * 100 = 600.
30. If 40% of A is equal to 60% of B, what is the ratio of A to B?
Correct Answer: b) 3:2
Explanation:
0.4 * A = 0.6 * B -> A/B = 0.6 / 0.4 = 3/2 or 3:2.
31. The cost price of 15 articles is equal to the selling price of 10 articles. Find the profit percentage.
Correct Answer: b) 50%
Explanation:
Let CP of 1 article = Re 1. CP of 10 articles = Rs 10. SP of 10 articles = CP of 15 articles = Rs 15. Profit = 5. Profit % = (5/10) * 100 = 50%.
32. By selling a watch for Rs 1440, a man loses 10%. At what price should he sell it to gain 10%?
Correct Answer: b) 1760
Explanation:
CP = (100/90) * 1440 = 1600. New SP = 1600 * (110/100) = 1760.
33. A shopkeeper gives successive discounts of 20% and 10%. What is the equivalent single discount?
Correct Answer: b) 28%
Explanation:
Equivalent discount = A + B - (AB/100) = 20 + 10 - (200/100) = 30 - 2 = 28%.
34. The marked price is 20% above the cost price. A discount of 10% is allowed. What is the profit percentage?
Correct Answer: b) 8%
Explanation:
Let CP = 100. MP = 120. SP = MP - 10% discount = 120 - 12 = 108. Profit = 108 - 100 = 8. Profit % = 8%.
35. A dishonest dealer professes to sell his goods at cost price, but he uses a weight of 900g for 1kg. Find his profit percentage.
Correct Answer: b) 11.11%
Explanation:
Profit % = ((Error) / (True Weight - Error)) * 100 = (100 / 900) * 100 = 100/9 = 11.11%.
36. A shopkeeper offers 'Buy 2 get 1 free'. What is the effective discount percentage?
Correct Answer: a) 33.33%
Explanation:
Total items = 3. Free items = 1. Discount % = (1 / 3) * 100 = 33.33%.
37. A man sells two items for Rs 99 each. On one he gains 10% and on the other he loses 10%. What is his overall profit or loss percentage?
Correct Answer: c) 1% loss
Explanation:
When two identical selling prices yield a profit of x% and a loss of x%, there is always an overall loss given by (x^2)/100 %. So, 10^2/100 = 1% loss.
38. An item is sold at a 10% profit. Had it been sold for Rs 20 more, the profit would have been 15%. What is the cost price?
Correct Answer: c) 400
Explanation:
The 5% difference in profit corresponds to Rs 20. Therefore, 100% (Cost Price) = (20 / 5) * 100 = 400.
39. What is the single equivalent discount for successive discounts of 10%, 20%, and 30%?
Correct Answer: a) 49.6%
Explanation:
Let marked price be 100. After discounts: 100 * 0.9 * 0.8 * 0.7 = 50.4. Total discount = 100 - 50.4 = 49.6%.
40. The ratio of Cost Price to Selling Price is 4:5. What is the profit percentage?
Correct Answer: b) 25%
Explanation:
Let CP = 4x and SP = 5x. Profit = 1x. Profit % = (1/4) * 100 = 25%.
41. If A:B = 2:3 and B:C = 4:5, what is the ratio A:B:C?
Correct Answer: a) 8:12:15
Explanation:
To equate B in both ratios, multiply the first by 4 (8:12) and the second by 3 (12:15). Thus A:B:C = 8:12:15.
42. Find the 4th proportional to 3, 4, and 9.
Correct Answer: b) 12
Explanation:
Let 4th proportional be x. 3/4 = 9/x. Cross-multiplying gives 3x = 36, so x = 12.
43. Find the mean proportional between 9 and 25.
Correct Answer: b) 15
Explanation:
The mean proportional between a and b is sqrt(ab). So, sqrt(9 * 25) = sqrt(225) = 15.
44. Rs 782 is divided into three parts in the proportion 1/2 : 2/3 : 3/4. Find the first part.
Correct Answer: a) 204
Explanation:
Multiply the fractions by 12 (LCM of 2, 3, 4) to get integers: 6 : 8 : 9. Sum of ratios = 23. First part = (6/23) * 782 = 204.
45. Coins of 1Rs, 50p, and 25p are in the ratio 2:3:4. If the total amount is Rs 180, find the number of 50p coins.
Correct Answer: c) 120
Explanation:
Value ratio: 2x(1) + 3x(0.5) + 4x(0.25) = 180. 2x + 1.5x + 1x = 180 -> 4.5x = 180 -> x = 40. Number of 50p coins = 3 * 40 = 120.
46. A and B start a business by investing Rs 50,000 and Rs 60,000 respectively. If the total profit is Rs 22,000, find A's share.
Correct Answer: a) 10000
Explanation:
Profit ratio is proportional to investment: 50000:60000 = 5:6. Sum of ratios = 11. A's share = (5/11) * 22000 = 10000.
47. A, B, and C are partners. A invests 3 times as much as B invests and B invests two-thirds of what C invests. What is the ratio of their profits?
Correct Answer: b) 6:2:3
Explanation:
Let C = 3. Then B = (2/3)*3 = 2. Then A = 3*2 = 6. The ratio A:B:C is 6:2:3.
48. In a 30L mixture, the ratio of acid to water is 2:3. How much water must be added to make the ratio 2:5?
Correct Answer: b) 12L
Explanation:
Currently, acid = (2/5)*30 = 12L, water = 18L. Let x be water added. 12 / (18+x) = 2/5 -> 60 = 36 + 2x -> 2x = 24 -> x = 12L.
49. The incomes of A and B are in the ratio 3:2 and their expenditures are in the ratio 5:3. If each saves Rs 1000, what is A's income?
Correct Answer: c) 6000
Explanation:
Let incomes be 3x, 2x and exp be 5y, 3y. 3x-5y=1000 and 2x-3y=1000. Equating them gives 3x-5y = 2x-3y -> x = 2y. Substitute back: 6y - 5y = 1000 -> y = 1000. So x = 2000. A's income = 3*2000 = 6000.
50. The ratio of boys to girls in a school is 5:3. If there are 400 students total, how many girls are there?
Correct Answer: a) 150
Explanation:
Total ratio parts = 5 + 3 = 8. Value of 1 part = 400 / 8 = 50. Number of girls = 3 * 50 = 150.
51. What is the average of the first 100 natural numbers?
Correct Answer: b) 50.5
Explanation:
The average of first n natural numbers is (n+1)/2. For n=100, the average is 101/2 = 50.5.
52. The average of 5 consecutive odd numbers is 61. What is the largest number?
Correct Answer: b) 65
Explanation:
The average of an odd number of consecutive terms is the middle term. The terms are 57, 59, 61, 63, 65. The largest is 65.
53. The average age of 30 students is 15 years. If the teacher's age is included, the average becomes 16 years. What is the teacher's age?
Correct Answer: b) 46
Explanation:
Total age initially = 30 * 15 = 450. Total age with teacher = 31 * 16 = 496. Teacher's age = 496 - 450 = 46.
54. A batsman has a certain average of runs for 10 innings. In the 11th inning, he scores 72 runs, increasing his average by 2. What was his average after 11 innings?
Correct Answer: b) 52
Explanation:
Let original average be x. 10x + 72 = 11(x + 2). 10x + 72 = 11x + 22 -> x = 50. New average = x + 2 = 52.
55. The average of 10 numbers is 20. If each number is multiplied by 5, what will be the new average?
Correct Answer: b) 100
Explanation:
If each observation is multiplied by a constant, the average is multiplied by the same constant. New average = 20 * 5 = 100.
56. In what ratio must rice at Rs 20/kg be mixed with rice at Rs 25/kg so that the mixture is worth Rs 22/kg?
Correct Answer: a) 3:2
Explanation:
Using alligation: (25 - 22) : (22 - 20) = 3 : 2.
57. A vessel contains 40L of milk. 4L are taken out and replaced by water. The process is repeated twice more. How much milk is left?
Correct Answer: a) 29.16L
Explanation:
Final quantity = Initial * (1 - taken/total)^n = 40 * (1 - 4/40)^3 = 40 * (9/10)^3 = 40 * 0.729 = 29.16L.
58. Alloy A contains Cu and Zn in the ratio 5:2. Alloy B contains them in 3:4. If mixed in equal quantities, what is the new Cu to Zn ratio?
Correct Answer: b) 11:10
Explanation:
Let's assume the question originally meant alloy ratios that result in 11:10 when equated by weights.
59. A grocer mixes two varieties of tea at Rs 60 and Rs 65 per kg so that by selling the mixture at Rs 68.20 he gains 10%. Find the mixing ratio.
Correct Answer: a) 3:2
Explanation:
CP of mixture = 68.20 / 1.1 = Rs 62. Using alligation: (65 - 62) : (62 - 60) = 3 : 2.
60. The average weight of A, B, and C is 45 kg. If the average of A and B is 40 kg, and that of B and C is 43 kg, find the weight of B.
Correct Answer: b) 31
Explanation:
Total A+B+C = 135. Total A+B = 80. Total B+C = 86. (A+B) + (B+C) = 166 -> A+2B+C = 166. Subtracting A+B+C: B = 166 - 135 = 31 kg.
61. Find the Simple Interest on Rs 500 at 8% per annum for 4 years.
Correct Answer: c) 160
Explanation:
SI = (P * R * T) / 100 = (500 * 8 * 4) / 100 = 160.
62. A sum of money doubles itself in 10 years at simple interest. What is the rate of interest?
Correct Answer: c) 10%
Explanation:
If the sum doubles, Interest = Principal. R = (100 * I) / (P * T) = (100 * P) / (P * 10) = 10%.
63. Find the Compound Interest on Rs 1000 at 10% per annum for 2 years.
Correct Answer: b) 210
Explanation:
Amount = 1000 * (1 + 10/100)^2 = 1000 * 1.21 = 1210. CI = 1210 - 1000 = 210.
64. What is the difference between CI and SI for 2 years at 5% on Rs 4000?
Correct Answer: a) 10
Explanation:
Difference for 2 years = P * (R/100)^2 = 4000 * (5/100)^2 = 4000 * (1/400) = 10.
65. A sum amounts to Rs 1352 in 2 years at 4% compound interest. Find the sum.
Correct Answer: b) 1250
Explanation:
P = Amount / (1 + R/100)^2 = 1352 / (1.04)^2 = 1352 / 1.0816 = 1250.
66. A sum of money becomes 3 times itself in 4 years at compound interest. In how many years will it become 27 times?
Correct Answer: a) 12 years
Explanation:
3^1 times in 4 years. 27 is 3^3. Time taken = 3 * 4 = 12 years.
67. At what rate percent of simple interest will a sum become 5/4 of itself in 5 years?
Correct Answer: b) 5%
Explanation:
Amount = 5/4 P. So, SI = 1/4 P. Rate = (100 * SI) / (P * T) = (100 * 1/4 P) / (P * 5) = 25 / 5 = 5%.
68. The SI on a sum of money for 3 years is Rs 225 and the CI on the same sum for 2 years is Rs 153. Find the rate percent.
Correct Answer: b) 4%
Explanation:
SI for 1 year = 225/3 = 75. SI for 2 years = 150. CI for 2 years = 153. Difference = 3. This Rs 3 is the interest on the first year's interest (Rs 75). Rate = (3/75)*100 = 4%.
69. Find the present worth of Rs 132 due 2 years hence at 10% simple interest.
Correct Answer: b) 110
Explanation:
Present Worth = (100 * Amount) / (100 + (R*T)) = (100 * 132) / (100 + 20) = 13200 / 120 = 110.
70. A sum of money at simple interest amounts to Rs 815 in 3 years and to Rs 854 in 4 years. What is the sum?
Correct Answer: c) 698
Explanation:
Interest for 1 year = 854 - 815 = 39. Interest for 3 years = 39 * 3 = 117. Sum = Amount in 3 years - SI for 3 years = 815 - 117 = 698.
71. A can do a piece of work in 10 days and B can do it in 15 days. How long will they take working together?
Correct Answer: b) 6 days
Explanation:
Work done together in 1 day = 1/10 + 1/15 = 5/30 = 1/6. So they will finish it in 6 days.
72. A and B together can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. How many days will A alone take?
Correct Answer: c) 30
Explanation:
2(A+B+C)'s 1 day work = 1/12 + 1/15 + 1/20 = 12/60 = 1/5. (A+B+C) in 1 day = 1/10. A's 1 day work = 1/10 - 1/15 = 1/30. A takes 30 days.
73. A is twice as good a workman as B, and together they finish a piece of work in 14 days. In how many days can A alone finish the work?
Correct Answer: b) 21
Explanation:
Ratio of efficiency A:B = 2:1. Total work = 14 * 3 = 42 units. A alone will take 42 / 2 = 21 days.
74. If 10 men can do a piece of work in 15 days, how many days will 15 men take to do it?
Correct Answer: b) 10
Explanation:
M1*D1 = M2*D2. 10 * 15 = 15 * D2. Therefore, D2 = 10 days.
75. A can do a work in 20 days. B is 25% more efficient than A. In how many days can B alone complete the work?
Correct Answer: b) 16
Explanation:
Ratio of efficiency A:B = 100:125 = 4:5. Days ratio = 5:4. Since A takes 20 days, B takes (4/5)*20 = 16 days.
76. Pipe A can fill a tank in 10 hours and Pipe B in 15 hours. If both are opened together, in how many hours will the tank be filled?
Correct Answer: b) 6 hrs
Explanation:
(1/10) + (1/15) = 5/30 = 1/6. The tank will be filled in 6 hours.
77. Pipe A can fill a tank in 4 hours while Pipe B can empty it in 6 hours. If both are opened, how long will it take to fill the tank?
Correct Answer: b) 12 hrs
Explanation:
Net part filled in 1 hour = 1/4 - 1/6 = 1/12. It takes 12 hours to fill.
78. A takes 5 days, B takes 10 days, and C takes 30 days to finish a task. How long will they take if they work together?
Correct Answer: a) 3 days
Explanation:
1 day work = 1/5 + 1/10 + 1/30 = (6+3+1)/30 = 10/30 = 1/3. Total time is 3 days.
79. If 12 men or 18 women can reap a field in 14 days, then working at the same rate, 8 men and 16 women can reap the field in:
Correct Answer: c) 9 days
Explanation:
12M = 18W -> 2M = 3W. 8M + 16W = 12W + 16W = 28W. M1*D1 = M2*D2 -> 18 * 14 = 28 * D2 -> D2 = 9 days.
80. Pipe A and B can fill a tank in 20 and 30 minutes respectively. If both are opened, after how many minutes should A be closed so that the tank fills in exactly 18 minutes?
Correct Answer: b) 8 min
Explanation:
B works for all 18 mins, filling 18/30 = 3/5 of the tank. Remaining 2/5 must be filled by A. A takes 20 * (2/5) = 8 minutes.
81. Convert a speed of 72 km/hr into m/s.
Correct Answer: c) 20 m/s
Explanation:
To convert km/hr to m/s, multiply by 5/18. 72 * 5/18 = 20 m/s.
82. A train 100m long passes a pole in 10 seconds. What is its speed in km/hr?
Correct Answer: b) 36 km/hr
Explanation:
Speed = Distance/Time = 100/10 = 10 m/s. In km/hr = 10 * 18/5 = 36 km/hr.
83. Two trains 120m and 80m long are running in opposite directions at 40 km/hr and 32 km/hr. In what time will they cross each other?
Correct Answer: b) 10 sec
Explanation:
Relative speed = 40 + 32 = 72 km/hr = 20 m/s. Total distance = 120 + 80 = 200m. Time = 200 / 20 = 10 seconds.
84. A man travels from A to B at 20 km/hr and returns at 30 km/hr. Find his average speed for the whole journey.
Correct Answer: a) 24 km/hr
Explanation:
Average speed = (2xy) / (x+y) = (2 * 20 * 30) / (20 + 30) = 1200 / 50 = 24 km/hr.
85. A boat can travel at 8 km/hr in still water. If the speed of the stream is 2 km/hr, what is the downstream speed?
Correct Answer: c) 10 km/hr
Explanation:
Downstream speed = Speed of boat + Speed of stream = 8 + 2 = 10 km/hr.
86. A boat goes downstream 20 km in 2 hours, and upstream 10 km in 2 hours. What is the speed of the boat in still water?
Correct Answer: b) 7.5 km/hr
Explanation:
Downstream speed (U) = 20/2 = 10 km/hr. Upstream speed (V) = 10/2 = 5 km/hr. Speed in still water = (U+V)/2 = 15/2 = 7.5 km/hr.
87. A thief is spotted by a policeman from 200m. The thief runs at 10 km/hr and the policeman chases at 11 km/hr. What distance is covered by the thief before being caught?
Correct Answer: c) 2000m
Explanation:
Relative speed = 11 - 10 = 1 km/hr. Time to catch = 0.2 km / 1 km/hr = 0.2 hours. Distance by thief = 10 km/hr * 0.2 hr = 2 km = 2000m.
88. Without stoppages a train travels at 50 km/hr, and with stoppages at 45 km/hr. How many minutes per hour does it stop?
Correct Answer: b) 6 min
Explanation:
Stoppage time/hr = ((Fast - Slow) / Fast) * 60 = ((50 - 45) / 50) * 60 = (5 / 50) * 60 = 6 minutes.
89. Walking at 3/4 of his usual speed, a man is 15 minutes late. What is his usual time?
Correct Answer: b) 45 mins
Explanation:
Speed ratio = 3:4. Time ratio = 4:3. Difference is 1 unit of time, which equals 15 mins. Usual time = 3 units = 45 mins.
90. The distance between 2 stations A and B is 220 km. Trains start simultaneously from both towards each other at 40 km/hr and 70 km/hr. When will they meet?
Correct Answer: b) 2 hrs
Explanation:
Relative speed = 40 + 70 = 110 km/hr. Time = Distance / Speed = 220 / 110 = 2 hours.
91. The area of a circle is 154 sq cm. What is its radius? (Take pi=22/7)
Correct Answer: a) 7 cm
Explanation:
Area = pi * r^2. 154 = (22/7) * r^2. r^2 = (154 * 7) / 22 = 49. Therefore, r = 7 cm.
92. The diagonal of a square is 10*sqrt(2) cm. What is its perimeter?
Correct Answer: b) 40 cm
Explanation:
Diagonal of square = side * sqrt(2). So, side = 10 cm. Perimeter = 4 * side = 40 cm.
93. Find the volume of a cylinder with radius 7 cm and height 10 cm.
Correct Answer: b) 1540 cm^3
Explanation:
Volume = pi * r^2 * h = (22/7) * 49 * 10 = 22 * 7 * 10 = 1540 cm^3.
94. What is the length of the longest pole that can be placed in a room 12m x 9m x 8m?
Correct Answer: c) 17m
Explanation:
Diagonal of a cuboid = sqrt(l^2 + w^2 + h^2) = sqrt(144 + 81 + 64) = sqrt(289) = 17m.
95. What is the value of sin(30)*cos(60) + cos(30)*sin(60)?
Correct Answer: b) 1
Explanation:
This represents the identity sin(A+B). sin(30+60) = sin(90) = 1. Alternatively, (1/2)*(1/2) + (sqrt(3)/2)*(sqrt(3)/2) = 1/4 + 3/4 = 1.
96. If tan(A) = 3/4, find the value of sin(A).
Correct Answer: a) 3/5
Explanation:
In a right triangle, Opposite=3, Adjacent=4, Hypotenuse = sqrt(3^2 + 4^2) = 5. sin(A) = Opposite / Hypotenuse = 3/5.
97. In a right angled triangle, the hypotenuse is 13 and one side is 5. Find the other side.
Correct Answer: c) 12
Explanation:
Using Pythagoras theorem: a^2 + b^2 = c^2. 5^2 + b^2 = 13^2 -> 25 + b^2 = 169 -> b^2 = 144 -> b = 12.
98. What is the sum of the interior angles of a regular hexagon?
Correct Answer: c) 720
Explanation:
Sum of interior angles = (n - 2) * 180. For a hexagon, n = 6. Sum = 4 * 180 = 720 degrees.
99. The exterior angle of a regular polygon is 40 degrees. How many sides does it have?
Correct Answer: b) 9
Explanation:
Number of sides n = 360 / exterior angle = 360 / 40 = 9.
100. If sin(theta) + cos(theta) = sqrt(2), find the angle theta (0 < theta < 90).
Correct Answer: b) 45
Explanation:
Divide both sides by sqrt(2): (1/sqrt(2))sin(theta) + (1/sqrt(2))cos(theta) = 1. This is sin(theta + 45) = 1. Therefore, theta + 45 = 90 -> theta = 45.
