Read each question, consider the options, then reveal the correct answer and explanation.
100 MCQs10 per page3 of 10
MCQ 21Work And Time
Five boys take 7 hours to pack 35 toys. At the same productivity, what equivalent workforce is required to pack 65 toys in 3 hours?
26 boys
39 boys
45 boys
21⅔ boys
Correct answerD — 21⅔ boys
Explanation
The original work uses 5×7=35 boy-hours for 35 toys, so productivity is one toy per boy-hour. Packing 65 toys in 3 hours requires 65/3=21⅔ equivalent boys. In practical staffing, at least 22 whole boys would be needed; the printed source item is mathematically incompatible with its integer options.
MCQ 22Work And Wages
A and B can complete a work alone in 8 and 12 days, respectively. They work on alternate days, starting with A, and receive ₹1280 for the completed work. What is A's share?
₹800
₹500
₹600
₹700
Correct answerA — ₹800
Explanation
Take total work as 24 units. A does 3 units per day and B does 2. In 8 days, four A-days and four B-days complete 20 units. On day 9 A completes 3 more units, leaving 1 unit, which B finishes in half a day. A works 5 full days and completes 15 of 24 units, so A receives 15/24×₹1280 = ₹800.
MCQ 23Number System
For every whole number n greater than 1, n^2(n^2 - 1) is always divisible by which of the following?
24
48
60
12
Correct answerD — 12
Explanation
Factor n^2(n^2 - 1) as n^2(n - 1)(n + 1). The three consecutive integers n - 1, n, n + 1 include a multiple of 3, and the expression always contains enough factors of 2 to make it divisible by 4. Hence it is always divisible by 12. It is not always divisible by 24; n = 2 gives exactly 12.
MCQ 24Partnership
A and B originally invest ₹20000 and ₹35000 and share profit in that ratio. C joins so that all three will share profit equally and pays a premium to compensate A and B. In what ratio should A and B divide the premium?
10:1
9:10
10:9
1:10
Correct answerD — 1:10
Explanation
Before C joins, A and B have profit shares 4/11 and 7/11. After admission, each partner receives 1/3. A sacrifices 4/11−1/3 = 1/33, while B sacrifices 7/11−1/3 = 10/33. Premium is divided according to sacrifice, so A:B = 1:10. This corrects the reversed ratio in the printed solution.
MCQ 25Square Root And Cube Root
Which of the following expressions are equivalent? I. (M/2 + 2N/3)² II. 4N²/9 + M²/4 + 2MN/3 III. (M/2 + 2N/3)(M/2 - 2N/3) IV. (1/4)(M + 4N/3)²
I and III only
I, II, and IV only
I and IV only
II and III only
Correct answerB — I, II, and IV only
Explanation
Expanding I gives M²/4 + 2MN/3 + 4N²/9, exactly the expression in II. Expanding IV also gives one-fourth of M² + 8MN/3 + 16N²/9, which simplifies to the same result. Expression III is a difference of squares, M²/4 - 4N²/9, so it is not equivalent. Hence I, II, and IV are equivalent.
MCQ 26Number System
A number leaves remainder 24 when divided by an unknown divisor. Twice the number leaves remainder 11 when divided by the same divisor. What is the divisor?
13
59
37
35
Correct answerC — 37
Explanation
If N leaves remainder 24 modulo d, then 2N leaves remainder equivalent to 48 modulo d. The problem says this remainder is 11, so 48 - 11 = 37 must be divisible by d. Also d must be greater than the original remainder 24. The only positive divisor of 37 greater than 24 is 37 itself.
MCQ 27Problems Based On Trains
A goods train and a passenger train move in the same direction on parallel tracks. The passenger train is twice as fast as the goods train. The driver of the goods train observes that the passenger train completely overtakes his train in 1 minute, while a passenger in the passenger train takes 2/3 minute to pass the goods train. Find the ratio of the goods train's length to the passenger train's length.
4:1
2:1
3:1
1:4
Correct answerB — 2:1
Explanation
Let the goods and passenger speeds be v and 2v, and their lengths be G and P. Their relative speed is v. Complete overtaking takes 1 minute, so G+P=v×1. A passenger in the faster train crosses only the goods train in 2/3 minute, so G=(2/3)v. Therefore P=v−(2/3)v=(1/3)v, and P=2:1.
MCQ 28Work And Wages
Four men and six women earn ₹1600 by completing a work in 5 days. Three men and seven women earn ₹1740 by completing the same work in 6 days. At the same wage-efficiency rates, how many days will seven men and six women take to earn ₹3760 for the same type of work?
6 days
8 days
10 days
12 days
Correct answerB — 8 days
Explanation
The first team's daily wages are ₹1600/5=₹320, so 4m+6w=320. The second team's daily wages are ₹1740/6=₹290, so 3m+7w=290. Solving gives one man's daily wage ₹50 and one woman's ₹20. Seven men and six women therefore earn 7×50+6×20=₹470 per day, so ₹3760 requires 3760/470=8 days.
MCQ 29Work And Time
Five men start a work that they could complete in 15 days. After 5 days, ten women join them and the work finishes 5 days later. If ten women alone had started the work, how many days would they need?
10 days
18 days
12 days
15 days
Correct answerD — 15 days
Explanation
Total work=5×15=75 man-days. In the first 5 days, the men do 25 man-days, leaving 50. During the next 5 days the combined team therefore works at 10 man-equivalents per day. Since the 5 men contribute 5, ten women are equivalent to 5 men. Ten women alone would need 75/5=15 days.
MCQ 30Simplification
Solve: 7059 - 2350 + 1936 = x × 50. Find x.
132.9
123.6
132.3
123.9
Correct answerA — 132.9
Explanation
First simplify the left side: 7059 - 2350 = 4709, and 4709 + 1936 = 6645. Hence 50x = 6645, so x = 6645/50 = 132.9. This item is a direct application of VBODMAS: addition and subtraction of equal precedence are handled from left to right before solving the resulting equation.
