Quantitative aptitude is a foundational assessment component in nearly all competitive examinations and corporate placement tests, designed to evaluate a candidate’s mathematical reasoning and numerical problem-solving efficiency. Basic quantitative aptitude encompasses core arithmetic areas including the number system, percentages, averages, ratio and proportion, and time-speed-distance mechanics. Mastery of these topics requires understanding underlying formulas, utilizing shortcut calculation methods, and developing logical deduction skills to process numerical data rapidly. Because speed and accuracy dictate exam performance, establishing a solid grasp of basic algebraic rules, fraction conversions, and mathematical theorems is essential before tackling advanced or higher-order analytical problems.
1. What is the unit digit of 7^105?
Correct Answer: c) 7
Explanation:
The cyclicity of 7 is 4 (7^1=7, 7^2=9, 7^3=3, 7^4=1). Dividing the power 105 by 4 gives a remainder of 1. Therefore, the unit digit is 7^1 = 7.
2. What is the sum of the first 50 natural numbers?
Correct Answer: c) 1275
Explanation:
The formula for the sum of the first n natural numbers is n(n + 1) / 2. For n = 50, Sum = 50 × 51 / 2 = 1275.
3. What is the remainder when 2^31 is divided by 5?
Correct Answer: c) 3
Explanation:
2^1 = 2, 2^2 = 4, 2^3 = 8 ≡ 3 (mod 5), 2^4 = 16 ≡ 1 (mod 5). Since 31 = 4 × 7 + 3, 2^31 ≡ 2^3 ≡ 8 ≡ 3 (mod 5).
4. Find the total number of prime factors in 2^3 × 5^2 × 7^1.
Correct Answer: c) 6
Explanation:
The total number of prime factors is the sum of the exponents of the prime bases: 3 + 2 + 1 = 6.
5. Which of the following numbers is a prime number?
Correct Answer: c) 137
Explanation:
91 = 7 × 13, 119 = 7 × 17, and 161 = 7 × 23. 137 has no divisors other than 1 and itself, making it a prime number.
6. Evaluate the expression: 15 + 6 ÷ 2 × 3 - 4.
Correct Answer: a) 20
Explanation:
Following BODMAS: Division first (6 ÷ 2 = 3), then Multiplication (3 × 3 = 9), then Addition/Subtraction (15 + 9 - 4 = 20).
7. Find the value of x if x / 16 = 64 / x.
Correct Answer: c) 32
Explanation:
Cross-multiplying gives x^2 = 16 × 64 = 1024. Taking the square root gives x = 32.
8. What least number must be added to 1056 so that the sum is completely divisible by 23?
Correct Answer: a) 2
Explanation:
Dividing 1056 by 23 leaves a remainder of 21. To make it completely divisible by 23, we need to add 23 - 21 = 2.
9. What is the sum of all even numbers from 1 to 40?
Correct Answer: c) 420
Explanation:
There are 20 even numbers from 1 to 40. The sum of the first n even numbers is n(n + 1). Sum = 20 × 21 = 420.
10. If a number is increased by 20% and then decreased by 20%, what is the net percentage change?
Correct Answer: c) 4% decrease
Explanation:
Net percentage change = +20 - 20 - (20 × 20) / 100 = -4%. Thus, there is a 4% decrease.
11. Find the HCF of 36 and 84.
Correct Answer: b) 12
Explanation:
36 = 12 × 3 and 84 = 12 × 7. The highest common factor between both numbers is 12.
12. Find the LCM of 12, 15, and 20.
Correct Answer: b) 60
Explanation:
Prime factorizations: 12 = 2^2 × 3, 15 = 3 × 5, 20 = 2^2 × 5. LCM = 2^2 × 3 × 5 = 60.
13. The product of two numbers is 2028 and their HCF is 13. How many such pairs of numbers are possible?
Correct Answer: b) 2
Explanation:
Let numbers be 13a and 13b (where a and b are co-prime). 13a × 13b = 2028 => ab = 12. Co-prime pairs (a,b) with product 12 are (1, 12) and (3, 4). Thus, 2 pairs exist.
14. Find the HCF of the fractions 2/3, 8/9, and 16/81.
Correct Answer: a) 2/81
Explanation:
HCF of fractions = (HCF of Numerators) / (LCM of Denominators) = HCF(2, 8, 16) / LCM(3, 9, 81) = 2 / 81.
15. Three bells toll together at intervals of 9, 12, and 15 minutes respectively. After how many hours will they toll together next?
Correct Answer: b) 3 hours
Explanation:
LCM(9, 12, 15) = 180 minutes. Converting minutes to hours: 180 / 60 = 3 hours.
16. Express 0.75 as a percentage.
Correct Answer: b) 75%
Explanation:
To convert a decimal to a percentage, multiply by 100: 0.75 × 100 = 75%.
17. What is 25% of 25% of 400?
Correct Answer: a) 25
Explanation:
Calculation: (25/100) × (25/100) × 400 = (1/4) × (1/4) × 400 = 25.
18. If A's salary is 25% more than B's salary, by what percentage is B's salary less than A's salary?
Correct Answer: a) 20%
Explanation:
Percentage reduction = [r / (100 + r)] × 100 = [25 / 125] × 100 = 20%.
19. In an examination, 35% marks are required to pass. A student gets 140 marks and fails by 35 marks. Find the maximum marks.
Correct Answer: c) 500
Explanation:
Passing marks = 140 + 35 = 175. If 35% = 175, then 100% = (175 / 35) × 100 = 500.
20. The population of a town increases by 10% annually. If the present population is 10,000, what will it be after 2 years?
Correct Answer: b) 12100
Explanation:
Population after 2 years = 10000 × (1 + 10/100)^2 = 10000 × 1.21 = 12,100.
21. If the price of sugar increases by 20%, by what percentage should a family reduce its consumption so that the expenditure remains unchanged?
Correct Answer: a) 16.67%
Explanation:
Reduction % = [r / (100 + r)] × 100 = [20 / 120] × 100 = 100 / 6 = 16.67%.
22. Two candidates contested an election. One got 60% of total votes and won by a majority of 1200 votes. Find total votes polled.
Correct Answer: b) 6000
Explanation:
Winner gets 60%, Loser gets 40%. Majority difference = 20%. Given 20% = 1200, Total votes (100%) = (1200 / 20) × 100 = 6000.
23. A number is first increased by 10% and then decreased by 10%. What is the net change in the number?
Correct Answer: b) 1% decrease
Explanation:
Net change = +10 - 10 - (10 × 10)/100 = -1%. Hence, there is a 1% decrease.
24. If 60% of (x - y) = 30% of (x + y), then y is what percent of x?
Correct Answer: a) 33.33%
Explanation:
60(x - y) = 30(x + y) => 2(x - y) = x + y => 2x - 2y = x + y => x = 3y. Therefore, y/x = 1/3 = 33.33%.
25. A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?
Correct Answer: c) 64%
Explanation:
Error = 5/3 - 3/5 = 16/15. Percentage error = [(16/15) / (5/3)] × 100 = (16/25) × 100 = 64%.
26. An article is bought for Rs. 400 and sold for Rs. 500. Find the profit percentage.
Correct Answer: b) 25%
Explanation:
Profit = 500 - 400 = Rs. 100. Profit % = (100 / 400) × 100 = 25%.
27. If the cost price of 15 articles is equal to the selling price of 12 articles, find the gain percentage.
Correct Answer: b) 25%
Explanation:
15 CP = 12 SP => SP/CP = 15/12 = 5/4. Gain = 5 - 4 = 1. Gain % = (1 / 4) × 100 = 25%.
28. A shopkeeper sells an item at a loss of 10%. If he had sold it for Rs. 60 more, he would have gained 10%. Find the cost price.
Correct Answer: b) Rs. 300
Explanation:
Difference in percentage = 10% - (-10%) = 20%. Given 20% of CP = Rs. 60 => CP = (60 / 20) × 100 = Rs. 300.
29. The marked price of an article is Rs. 800. It is sold at two successive discounts of 10% and 20%. Find the selling price.
Correct Answer: b) Rs. 576
Explanation:
SP = Marked Price × (1 - d1/100) × (1 - d2/100) = 800 × 0.9 × 0.8 = Rs. 576.
30. By selling a watch for Rs. 1440, a man loses 10%. At what price should he sell it to gain 10%?
Correct Answer: b) Rs. 1760
Explanation:
90% of CP = 1440 => CP = 1600. To gain 10%, desired SP = 110% of 1600 = 1.1 × 1600 = Rs. 1760.
31. Find the single discount equivalent to two successive discounts of 20% and 10%.
Correct Answer: a) 28%
Explanation:
Equivalent discount = d1 + d2 - (d1 × d2)/100 = 20 + 10 - (200/100) = 28%.
32. A dishonest dealer professes to sell goods at cost price, but uses a weight of 900 grams for a 1 kg weight. Find gain percentage.
Correct Answer: b) 11.11%
Explanation:
Gain % = [Error / (True Value - Error)] × 100 = [100 / (1000 - 100)] × 100 = 100 / 9 = 11.11%.
33. If cost price is Rs. 250 and selling price is Rs. 200, what is the loss percentage?
Correct Answer: b) 20%
Explanation:
Loss = 250 - 200 = Rs. 50. Loss % = (50 / 250) × 100 = 20%.
34. A person buys 12 pens for Rs. 10 and sells 10 pens for Rs. 12. Find his profit percentage.
Correct Answer: c) 44%
Explanation:
CP of 1 pen = 10/12 = 5/6. SP of 1 pen = 12/10 = 6/5. Profit % = [(6/5 - 5/6) / (5/6)] × 100 = [(11/30) / (5/6)] × 100 = 44%.
35. After allowing a discount of 20% on marked price, a trader makes a profit of 20%. If CP is Rs. 500, what is the marked price?
Correct Answer: c) Rs. 750
Explanation:
MP × 0.80 = CP × 1.20 => MP × 0.80 = 500 × 1.20 = 600 => MP = 600 / 0.80 = Rs. 750.
36. Find the Simple Interest on Rs. 5000 at 10% per annum for 3 years.
Correct Answer: b) Rs. 1500
Explanation:
SI = (P × R × T) / 100 = (5000 × 10 × 3) / 100 = Rs. 1500.
37. At what rate per annum simple interest will a sum of money double itself in 8 years?
Correct Answer: b) 12.5%
Explanation:
If a sum doubles, SI = Principal = P. P = (P × R × 8) / 100 => R = 100 / 8 = 12.5%.
38. Find the Compound Interest on Rs. 10000 at 10% per annum for 2 years, compounded annually.
Correct Answer: b) Rs. 2100
Explanation:
Amount = 10000 × (1.1)^2 = 12100. CI = Amount - Principal = 12100 - 10000 = Rs. 2100.
39. What is the difference between SI and CI on Rs. 5000 at 10% per annum for 2 years?
Correct Answer: b) Rs. 50
Explanation:
Difference for 2 years = P × (R / 100)^2 = 5000 × (10 / 100)^2 = 5000 × 0.01 = Rs. 50.
40. In how many years will a sum of money triple itself at 20% simple interest per annum?
Correct Answer: b) 10 years
Explanation:
For money to triple, SI = 2P. 2P = (P × 20 × T) / 100 => T = 200 / 20 = 10 years.
41. A sum becomes 4 times in 3 years at compound interest. In how many years will it become 16 times at the same rate?
Correct Answer: a) 6 years
Explanation:
4^1 times in 3 years. Since 16 = 4^2, the time required will be 2 × 3 = 6 years.
42. If Rs. 8000 amounts to Rs. 9261 in 3 years at compound interest compounded annually, find the rate of interest per annum.
Correct Answer: b) 5%
Explanation:
(1 + R/100)^3 = 9261 / 8000 = (21/20)^3 => 1 + R/100 = 21/20 => R/100 = 1/20 => R = 5%.
43. Simple interest on a sum of money for 2 years at 5% p.a. is Rs. 400. What is the principal amount?
Correct Answer: b) Rs. 4000
Explanation:
P = (SI × 100) / (R × T) = (400 × 100) / (5 × 2) = 40000 / 10 = Rs. 4000.
44. A sum of money at simple interest amounts to Rs. 800 in 3 years and Rs. 900 in 4 years. Find the principal.
Correct Answer: b) Rs. 500
Explanation:
SI for 1 year = 900 - 800 = Rs. 100. SI for 3 years = 300. Principal = Amount - SI = 800 - 300 = Rs. 500.
45. What will be the compound interest on Rs. 1000 at 20% per annum for 1.5 years, compounded half-yearly?
Correct Answer: b) Rs. 331
Explanation:
Half-yearly rate = 10%, time periods n = 3. Amount = 1000 × (1.1)^3 = 1331. CI = 1331 - 1000 = Rs. 331.
46. If A : B = 2 : 3 and B : C = 4 : 5, find A : B : C.
Correct Answer: a) 8:12:15
Explanation:
A : B = 2×4 : 3×4 = 8 : 12. B : C = 4×3 : 5×3 = 12 : 15. Thus, A : B : C = 8 : 12 : 15.
47. If 2A = 3B = 4C, find A : B : C.
Correct Answer: c) 6:4:3
Explanation:
LCM of 2, 3, 4 is 12. Dividing 12 by coefficients: A = 12/2 = 6, B = 12/3 = 4, C = 12/4 = 3. A:B:C = 6:4:3.
48. Two numbers are in ratio 3 : 5. If 9 is subtracted from each, ratio becomes 12 : 23. Find the smaller number.
Correct Answer: a) 33
Explanation:
(3x - 9) / (5x - 9) = 12 / 23 => 69x - 207 = 60x - 108 => 9x = 99 => x = 11. Smaller number = 3 × 11 = 33.
49. Divide Rs. 1200 among A, B, and C in the ratio 2 : 3 : 5. What is B's share?
Correct Answer: b) Rs. 360
Explanation:
Total ratio units = 2 + 3 + 5 = 10. B's share = (3 / 10) × 1200 = Rs. 360.
50. What is the fourth proportional to 4, 9, and 12?
Correct Answer: c) 27
Explanation:
4 / 9 = 12 / x => 4x = 108 => x = 27.
51. Find the mean proportional between 9 and 25.
Correct Answer: b) 15
Explanation:
Mean proportional = √(9 × 25) = √225 = 15.
52. The ratio of two numbers is 4 : 5 and their sum is 180. Find the greater number.
Correct Answer: c) 100
Explanation:
4x + 5x = 180 => 9x = 180 => x = 20. Greater number = 5 × 20 = 100.
53. A bag contains 50p, 25p, and 10p coins in ratio 5:9:4 amounting to Rs. 206. Find the number of 50p coins.
Correct Answer: a) 200
Explanation:
Values: 0.5(5x) + 0.25(9x) + 0.10(4x) = 2.5x + 2.25x + 0.40x = 5.15x = 206 => x = 40. Number of 50p coins = 5 × 40 = 200.
54. Find the average of the first 10 prime numbers.
Correct Answer: a) 12.9
Explanation:
First 10 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Sum = 129. Average = 129 / 10 = 12.9.
55. The average of 5 numbers is 27. If one number is excluded, the average becomes 25. What is the excluded number?
Correct Answer: b) 35
Explanation:
Sum of 5 numbers = 5 × 27 = 135. Sum of remaining 4 numbers = 4 × 25 = 100. Excluded number = 135 - 100 = 35.
56. The average weight of 8 persons increases by 1.5 kg when a new person comes in place of one weighing 65 kg. Find weight of new person.
Correct Answer: b) 77 kg
Explanation:
Total increase in weight = 8 × 1.5 = 12 kg. Weight of new person = 65 + 12 = 77 kg.
57. The average score of 10 students is 80. Later, it was found that a score of 45 was misread as 54. Find correct average.
Correct Answer: a) 79.1
Explanation:
Difference = 45 - 54 = -9. Correction in average = -9 / 10 = -0.9. Correct average = 80 - 0.9 = 79.1.
58. Find the average of all multiples of 5 between 1 and 100.
Correct Answer: b) 50
Explanation:
Multiples of 5 between 1 and 100 are 5, 10, ..., 95. Average = (First term + Last term) / 2 = (5 + 95) / 2 = 50.
59. The average age of 30 students is 15 years. Including teacher's age increases average by 1 year. Find teacher's age.
Correct Answer: c) 46 years
Explanation:
Total age with teacher = 31 × 16 = 496. Total age without teacher = 30 × 15 = 450. Teacher's age = 496 - 450 = 46 years.
60. Average temperature for Mon, Tue, Wed was 40°C. For Tue, Wed, Thu was 41°C. If Thu was 42°C, find Monday's temperature.
Correct Answer: b) 39°C
Explanation:
(T + W + Th) - (M + T + W) = (3 × 41) - (3 × 40) => Th - M = 3. Given Th = 42, M = 42 - 3 = 39°C.
61. The ratio of present ages of A and B is 4 : 5. Six years hence, ratio will be 5 : 6. Find A's present age.
Correct Answer: b) 24 years
Explanation:
(4x + 6)/(5x + 6) = 5/6 => 24x + 36 = 25x + 30 => x = 6. A's age = 4 × 6 = 24 years.
62. A father is 3 times as old as his son. 10 years ago, he was 5 times as old as his son. Find the present age of the son.
Correct Answer: b) 20 years
Explanation:
Father = 3x, Son = x. 3x - 10 = 5(x - 10) => 3x - 10 = 5x - 50 => 2x = 40 => x = 20 years.
63. Sum of ages of mother and daughter is 50 years. 5 years ago, mother was 7 times as old as daughter. Find mother's present age.
Correct Answer: b) 40 years
Explanation:
5 years ago, sum of ages = 50 - 10 = 40. 7x + 1x = 40 => 8x = 40 => x = 5. Mother's age 5 yrs ago = 35 => Present age = 40.
64. A is 2 years older than B who is twice as old as C. If total of their ages is 27, how old is B?
Correct Answer: c) 10 years
Explanation:
Let C = x, B = 2x, A = 2x + 2. x + 2x + 2x + 2 = 27 => 5x = 25 => x = 5. B's age = 2 × 5 = 10 years.
65. Ratio of present ages of P and Q is 3:4. 4 years ago, sum of their ages was 27. What is Q's present age?
Correct Answer: c) 20 years
Explanation:
Present sum of ages = 27 + 8 = 35. 3x + 4x = 35 => 7x = 35 => x = 5. Q's age = 4 × 5 = 20 years.
66. A can do a work in 10 days and B can do it in 15 days. In how many days can both complete it together?
Correct Answer: b) 6 days
Explanation:
Time = (A × B) / (A + B) = (10 × 15) / (10 + 15) = 150 / 25 = 6 days.
67. A and B together finish a work in 12 days. B alone finishes it in 30 days. In how many days can A alone finish it?
Correct Answer: b) 20 days
Explanation:
A's 1 day work = 1/12 - 1/30 = (5 - 2)/60 = 3/60 = 1/20. So A takes 20 days.
68. A is twice as efficient as B. If together they finish a work in 12 days, how long will A alone take to finish it?
Correct Answer: b) 18 days
Explanation:
Efficiency ratio A:B = 2:1. Total efficiency = 3. Total work = 3 × 12 = 36 units. Time for A = 36 / 2 = 18 days.
69. If 12 men can build a wall in 15 days, how many men are required to build the same wall in 10 days?
Correct Answer: b) 18
Explanation:
M1 × D1 = M2 × D2 => 12 × 15 = M2 × 10 => 180 = 10 × M2 => M2 = 18 men.
70. Pipe A fills a tank in 6 hours and Pipe B empties it in 8 hours. Opened together, in how many hours is the tank filled?
Correct Answer: d) 24 hours
Explanation:
Net filling rate per hour = 1/6 - 1/8 = (4 - 3) / 24 = 1/24. Thus, it takes 24 hours to fill the tank.
71. A completes a work in 20 days. He works for 5 days and B finishes remaining work in 15 days. How long will B take alone?
Correct Answer: b) 20 days
Explanation:
A's 5 days work = 5/20 = 1/4. Remaining work = 3/4. B completes 3/4 work in 15 days => Total time for B = 15 × (4/3) = 20 days.
72. 8 men or 12 women can do a work in 25 days. In how many days can 6 men and 11 women do the same work?
Correct Answer: b) 15 days
Explanation:
8M = 12W => 1M = 1.5W. 6M + 11W = 6(1.5) + 11 = 20W. 12W × 25 = 20W × D => D = 300 / 20 = 15 days.
73. A, B and C can complete a job in 10, 12 and 15 days respectively. Working together, they finish it in:
Correct Answer: b) 4 days
Explanation:
Combined rate = 1/10 + 1/12 + 1/15 = (6 + 5 + 4) / 60 = 15 / 60 = 1/4. Time = 4 days.
74. Pipe A fills a cistern in 4 hours, B in 6 hours. Opened alternately for 1 hr starting with A, how long to fill the cistern?
Correct Answer: b) 4 hours 40 min
Explanation:
In 2 hours, filled = 1/4 + 1/6 = 5/12. In 4 hours, filled = 10/12 = 5/6. Remaining = 1/6. A takes (1/6)/(1/4) = 2/3 hr = 40 min. Total = 4 hrs 40 min.
75. A and B do a work in 8 days, B and C in 12 days, C and A in 24 days. In how many days can A, B, C together finish it?
Correct Answer: b) 8 days
Explanation:
2(A + B + C) = 1/8 + 1/12 + 1/24 = (3 + 2 + 1)/24 = 6/24 = 1/4 => A + B + C = 1/8. Time = 8 days.
76. Convert 72 km/h into meters per second (m/s).
Correct Answer: b) 20 m/s
Explanation:
Speed in m/s = 72 × (5 / 18) = 20 m/s.
77. A car covers a distance of 300 km in 5 hours. What is its speed in km/h?
Correct Answer: b) 60 km/h
Explanation:
Speed = Distance / Time = 300 / 5 = 60 km/h.
78. A train 150 meters long crosses a pole in 9 seconds. Find the speed of the train in km/h.
Correct Answer: b) 60 km/h
Explanation:
Speed = 150 / 9 m/s = (50 / 3) m/s. Converting to km/h: (50 / 3) × (18 / 5) = 60 km/h.
79. A man travels at 60 km/h from A to B and returns at 40 km/h. Find his average speed for the whole journey.
Correct Answer: a) 48 km/h
Explanation:
Average speed = (2xy) / (x + y) = (2 × 60 × 40) / (60 + 40) = 4800 / 100 = 48 km/h.
80. Two trains 100m and 120m long run in opposite directions at 42 km/h and 30 km/h. Time to cross each other is:
Correct Answer: c) 11 seconds
Explanation:
Relative speed = 42 + 30 = 72 km/h = 20 m/s. Total distance = 100 + 120 = 220 m. Time = 220 / 20 = 11 seconds.
81. A train running at 54 km/h crosses a platform 200 m long in 20 seconds. What is the length of the train?
Correct Answer: b) 100 m
Explanation:
Speed = 54 × (5/18) = 15 m/s. Total distance covered = 15 × 20 = 300 m. Train length = 300 - 200 = 100 m.
82. In a 100 m race, A beats B by 10 m or 2 seconds. What is A's time to complete the race?
Correct Answer: b) 18 seconds
Explanation:
B covers 10 m in 2 seconds => B's speed = 5 m/s. B's total time for 100 m = 100 / 5 = 20 s. A's time = 20 - 2 = 18 seconds.
83. A boat travels at 12 km/h in still water. If stream speed is 3 km/h, find time taken to travel 45 km downstream.
Correct Answer: b) 3 hours
Explanation:
Downstream speed = 12 + 3 = 15 km/h. Time = Distance / Speed = 45 / 15 = 3 hours.
84. A man rows upstream at 8 km/h and downstream at 14 km/h. Find speed of the man in still water.
Correct Answer: b) 11 km/h
Explanation:
Speed in still water = (Downstream speed + Upstream speed) / 2 = (14 + 8) / 2 = 11 km/h.
85. Walking at 3/4 of usual speed, a man is 20 minutes late to office. Find his usual time.
Correct Answer: c) 60 minutes
Explanation:
New time = 4/3 of usual time. Extra time = (4/3 - 1) of usual time = 1/3 of usual time = 20 min. Usual time = 60 minutes.
86. In what ratio must sugar at Rs. 40/kg be mixed with sugar at Rs. 55/kg to produce a mixture worth Rs. 45/kg?
Correct Answer: a) 2:1
Explanation:
By alligation rule: Ratio = (55 - 45) : (45 - 40) = 10 : 5 = 2 : 1.
87. A vessel contains 60 liters of milk. 12 liters are taken out and replaced with water, repeated once more. Milk left is:
Correct Answer: b) 38.4 liters
Explanation:
Remaining milk = 60 × (1 - 12/60)^2 = 60 × (4/5)^2 = 60 × 16 / 25 = 38.4 liters.
88. A 40-liter mixture contains milk and water in ratio 3 : 1. How much water must be added to make the ratio 1 : 1?
Correct Answer: c) 20 liters
Explanation:
Milk = 30L, Water = 10L. For 1:1 ratio, total water needed = 30L. Additional water needed = 30 - 10 = 20 liters.
89. In what ratio must water be mixed with milk costing Rs. 60 per liter to get a mixture worth Rs. 50 per liter?
Correct Answer: a) 1:5
Explanation:
Cost of water = 0. By alligation: Water : Milk = (60 - 50) : (50 - 0) = 10 : 50 = 1 : 5.
90. Two alloys contain copper and zinc in ratio 2:3 and 4:1. Ratio to mix them to get an alloy with equal copper and zinc is:
Correct Answer: b) 3:1
Explanation:
Copper fraction in A = 2/5, in B = 4/5, in target = 1/2. Ratio = (4/5 - 1/2) : (1/2 - 2/5) = (3/10) : (1/10) = 3 : 1.
91. Area of a rectangle is 180 cm² and its length is 15 cm. Find its perimeter.
Correct Answer: b) 54 cm
Explanation:
Breadth = 180 / 15 = 12 cm. Perimeter = 2(length + breadth) = 2(15 + 12) = 54 cm.
92. The side of a square is increased by 20%. By what percentage does its area increase?
Correct Answer: b) 44%
Explanation:
Net percentage change in area = 20 + 20 + (20 × 20)/100 = 44%.
93. What is the area of a circle whose circumference is 44 cm?
Correct Answer: b) 154 cm²
Explanation:
Circumference 2πr = 44 => 2 × (22/7) × r = 44 => r = 7 cm. Area = πr^2 = (22/7) × 49 = 154 cm².
94. Find the volume of a cube whose total surface area is 294 cm².
Correct Answer: b) 343 cm³
Explanation:
Total Surface Area = 6a^2 = 294 => a^2 = 49 => side a = 7 cm. Volume = a^3 = 7^3 = 343 cm³.
95. Find the length of the longest pole that can be placed in a room of dimensions 12m × 9m × 8m.
Correct Answer: c) 17 m
Explanation:
Longest pole = Diagonal = √(l^2 + b^2 + h^2) = √(144 + 81 + 64) = √289 = 17 m.
96. Radius and height of a cylinder are 7 cm and 10 cm respectively. Find its total surface area.
Correct Answer: b) 748 cm²
Explanation:
TSA = 2πr(h + r) = 2 × (22/7) × 7 × (10 + 7) = 44 × 17 = 748 cm².
97. In how many different ways can the letters of the word 'LEADER' be arranged?
Correct Answer: b) 360
Explanation:
Word has 6 letters with 'E' repeating 2 times. Total permutations = 6! / 2! = 720 / 2 = 360.
98. In how many ways can a committee of 3 people be chosen from 6 candidates?
Correct Answer: c) 20
Explanation:
Combinations = 6C3 = (6 × 5 × 4) / (3 × 2 × 1) = 20.
99. Two unbiased coins are tossed simultaneously. What is the probability of getting at least one head?
Correct Answer: c) 3/4
Explanation:
Sample space = {HH, HT, TH, TT}. Favorable outcomes for at least one head = {HH, HT, TH} (3 out of 4). Probability = 3/4.
100. A card is drawn at random from a standard pack of 52 cards. What is the probability that it is a King?
Correct Answer: a) 1/13
Explanation:
Number of Kings = 4, Total cards = 52. Probability = 4 / 52 = 1/13.
