A group of men decided to do a work in 10 days, but 5 of them became absent. If the rest of the group did the work in 12 days, find the original number of men. MCQ with Answer and Explanation

A group of men decided to do a work in 10 days, but 5 of them became absent. If the rest of the group did the work in 12 days, find the original number of men.
A. 35
B. 40
C. 30
D. 25
Answer: Option C
Solution (By JKSSB Mock Tests)
Let the original number of men be x. Using M1 * D1 = M2 * D2: x * 10 = (x - 5) * 12 => 10x = 12x - 60 => 2x = 60 => x = 30.

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Practice More Time and Work Questions

Question #1
A and B together can complete a piece of work in 8 days. If A alone can complete the same work in 12 days, in how many days can B alone complete it?
A. 20 days
B. 24 days
C. 16 days
D. 18 days

Correct Answer: Option B


Explanation:
Total work = LCM(8, 12) = 24 units. Combined efficiency of A and B = 3. Efficiency of A = 2. Efficiency of B = 3 - 2 = 1. Time taken by B alone = 24 / 1 = 24 days.

This question belongs to: Maths Time and Work
Question #2
A can complete a work in 14 days and B in 37 days. If both work together, in how many days will the work be completed?
A. 10.16
B. 17.66
C. 15.16
D. 12.66

Correct Answer: Option A


Explanation:
Combined rate = 1/14 + 1/37. Time = 10.16 days.

This question belongs to: Maths Time and Work
Question #3
A can build a wall in 30 days, while B can destroy it in 40 days. If they work on alternate days starting with A, in how many days will the wall be built?
A. 235 days
B. 233 days
C. 240 days
D. 237 days

Correct Answer: Option B


Explanation:
Total work = LCM(30, 40) = 120 units. Efficiency of A = +4, B = -3. In 2 days, net work = 4 - 3 = 1 unit. We look for when the work reaches 120 - 4 = 116 units. 116 units are done in 116 * 2 = 232 days. On the 233rd day, A works and completes 4 units, making total work 116 + 4 = 120 units. Thus, the wall is completed in 233 days.

This question belongs to: Maths Time and Work