22 men can complete a work in 14 days. If 27 men work at the same rate, the work will be completed in: MCQ with Answer and Explanation
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Question #1
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A can build a wall in 20 days, while B can destroy it in 30 days. If they work on alternate days starting with A, in how many days will the wall be completely built?
Correct Answer: Option B
Explanation:
Total work = LCM(20, 30) = 60 units. Efficiency of A = +3, B = -2. In 2 days (A then B), net work done = 3 - 2 = 1 unit. We need to reach 60 units. Since A can add 3 units on his turn, we find when work reaches 60 - 3 = 57 units. 57 units will be done in 57 * 2 = 114 days. On the 115th day, A works and completes 3 units, making the total work 57 + 3 = 60 units. So, the wall is built in 115 days.
Total work = LCM(20, 30) = 60 units. Efficiency of A = +3, B = -2. In 2 days (A then B), net work done = 3 - 2 = 1 unit. We need to reach 60 units. Since A can add 3 units on his turn, we find when work reaches 60 - 3 = 57 units. 57 units will be done in 57 * 2 = 114 days. On the 115th day, A works and completes 3 units, making the total work 57 + 3 = 60 units. So, the wall is built in 115 days.
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Maths
Time and Work
Question #2
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If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
Correct Answer: Option A
Explanation:
Total work = 10 * (6M + 8B) = 2 * (26M + 48B) => 60M + 80B = 52M + 96B => 8M = 16B => 1M = 2B. Total work in terms of boys = 10 * (6*2B + 8B) = 10 * 20B = 200 boy-days. Efficiency of 15 men and 20 boys = 15*2B + 20B = 50B. Time taken = 200 / 50 = 4 days.
Total work = 10 * (6M + 8B) = 2 * (26M + 48B) => 60M + 80B = 52M + 96B => 8M = 16B => 1M = 2B. Total work in terms of boys = 10 * (6*2B + 8B) = 10 * 20B = 200 boy-days. Efficiency of 15 men and 20 boys = 15*2B + 20B = 50B. Time taken = 200 / 50 = 4 days.
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Maths
Time and Work
Question #3
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A can complete a work in 14 days and B in 15 days. If they work together, the work will be completed in:
Correct Answer: Option A
Explanation:
Combined rate = 1/14 + 1/15. Required time = 7.24 days.
Combined rate = 1/14 + 1/15. Required time = 7.24 days.
This question belongs to:
Maths
Time and Work
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