Read each question, consider the options, then reveal the correct answer and explanation.
100 MCQs10 per page10 of 10
MCQ 91Work And Time
For a fixed job and constant individual speed, which graph correctly represents the relationship between the number of men x and the number of days y required?
A straight line through the origin
A horizontal straight line
A decreasing rectangular hyperbola, y=k/x
An increasing straight line
Correct answerC — A decreasing rectangular hyperbola, y=k/x
Explanation
For fixed work, men×days is constant, so xy=k and y=k/x. As the number of men increases, required days decrease inversely. The graph is a decreasing rectangular hyperbola and approaches, but does not touch, either axis.
MCQ 92Percentage
Rice price falls by 6.25%, allowing one extra kilogram to be bought for ₹120. What is the reduced price per kilogram?
₹9 per kg
₹5.50 per kg
₹19 per kg
₹7.50 per kg
Correct answerD — ₹7.50 per kg
Explanation
A 6.25% fall is a reduction of 1/16, so the new price is 15/16 of the old price. If the old price is p, quantities are 120/p and 120/(15p/16)=128/p. Their difference 8/p equals 1, so p=₹8 and the reduced price is ₹7.50.
Express every number in prime factors: 4=2², 20=2²·5, 12=2²·3, 15=3·5, 16=2⁴, and 9=3². Combining exponents causes all variable-dependent powers to cancel. The remaining constant factor is 2^(-2)·5^(-3)=1/(4·125)=1/500.
MCQ 94Pipes And Cisterns
Three inlet taps have diameters 1 cm, 4/3 cm, and 2 cm. Their flow rates are proportional to the squares of their diameters. The largest tap alone fills the tank in 61 minutes. How long will all three together take?
44 minutes
45 minutes
36 minutes
46 minutes
Correct answerC — 36 minutes
Explanation
Flow-rate weights are 1²:(4/3)²:2² = 1:16/9:4. Their sum is 61/9. The largest tap has weight 4 and rate 1/61 tank per minute, so the combined rate is (61/9)/4×1/61=1/36. Therefore all three fill the tank in 36 minutes.
MCQ 95Unitary Method
Twenty men complete one-third of a work in 20 days. How many additional men are needed to finish the remaining two-thirds in 25 days?
10
12
15
20
Correct answerB — 12
Explanation
One-third requires 20×20 = 400 man-days, so the whole work requires 1200 man-days. The remaining two-thirds require 800 man-days. In 25 days, 800/25 = 32 men are needed, so 12 additional men must join the original 20.
MCQ 96Work And Time
A alone takes 25 days more than A and B together, while B alone takes 49 days more than A and B together. How long do A and B take together?
25 days
35 days
15 days
45 days
Correct answerB — 35 days
Explanation
For this standard relation, if individual excess times over the joint time are 25 and 49 days, the joint time is √(25×49)=35 days. Algebraically, setting joint time t leads to 1/(t+25)+1/(t+49)=1/t, which gives t=35.
MCQ 97Average
The average age of two boys and their father exceeds the average age of the boys and their mother by 3 years. The four-person average is 19 years, and the boys' average is 5.5 years. What are the father's and mother's ages?
35 years and 32 years
37 years and 28 years
47 years and 38 years
50 years and 41 years
Correct answerB — 37 years and 28 years
Explanation
The boys together are 11 years old, while the family total is 4×19 = 76, so father+mother = 65. The difference between the two three-person averages is 3, so father−mother = 9. Solving gives father 37 and mother 28.
MCQ 98Profit And Loss
A person buys a book for ₹200 and sells it for ₹225. What is the gain percentage?
12.5%
13%
14%
18.4%
Correct answerA — 12.5%
Explanation
Profit = selling price - cost price = 225 - 200 = ₹25. Profit percentage is calculated on cost price: (25/200)×100 = 12.5%. The cost price is always the comparison base unless a question explicitly states otherwise.
MCQ 99Number System
How many integers strictly between -11 and 11 are multiples of 2 or 3?
15
11
14
16
Correct answerA — 15
Explanation
The integers are -10 through 10. Multiples of 2 are -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, and multiples of 3 are -9, -6, -3, 0, 3, 6, 9. Taking the union without double-counting common multiples gives 15 integers.
MCQ 100Simple And Decimal Fractions
Evaluate (16/23) × (47/288) × (92/141).
4/27
2/29
2/27
3/28
Correct answerC — 2/27
Explanation
Factor and cancel before multiplying. Since 92 = 4×23, the 23 cancels; 141 = 3×47, so 47 cancels. The expression becomes (16×4)/(288×3) = 64/864 = 2/27. Cross-cancellation makes fraction multiplication much faster.
