12 men can complete a work in 22 days. If 16 men work at the same rate, in how many days will the work be completed? MCQ with Answer and Explanation
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Question #1
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A can do a piece of work in 20 days and B in 30 days. They work together for some time and then B leaves. If A completes the remaining work in 5 days, for how many days did they work together?
Correct Answer: Option C
Explanation:
Total work = LCM(20, 30) = 60 units. Efficiency of A = 3, B = 2. A worked alone for 5 days: work done = 5 * 3 = 15 units. Remaining work = 60 - 15 = 45 units. This was completed by A and B together. Combined efficiency = 3 + 2 = 5 units/day. Number of days they worked together = 45 / 5 = 9 days.
Total work = LCM(20, 30) = 60 units. Efficiency of A = 3, B = 2. A worked alone for 5 days: work done = 5 * 3 = 15 units. Remaining work = 60 - 15 = 45 units. This was completed by A and B together. Combined efficiency = 3 + 2 = 5 units/day. Number of days they worked together = 45 / 5 = 9 days.
This question belongs to:
Maths
Time and Work
Question #2
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A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how many days will A and B together complete the work?
Correct Answer: Option C
Explanation:
A's 10-day work = 10/80 = 1/8. Remaining work = 7/8. B completes 7/8 work in 42 days, so B completes full work in 42 * (8/7) = 48 days. Combined 1-day work = 1/80 + 1/48 = (3 + 5)/240 = 8/240 = 1/30. They finish together in 30 days.
A's 10-day work = 10/80 = 1/8. Remaining work = 7/8. B completes 7/8 work in 42 days, so B completes full work in 42 * (8/7) = 48 days. Combined 1-day work = 1/80 + 1/48 = (3 + 5)/240 = 8/240 = 1/30. They finish together in 30 days.
This question belongs to:
Maths
Time and Work
Question #3
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A can complete a work in 22 days and B in 44 days. After working together for 5 days, what percentage of work remains?
Correct Answer: Option B
Explanation:
Remaining work = (1 - 5*(1/22+1/44))×100 = 65.91%.
Remaining work = (1 - 5*(1/22+1/44))×100 = 65.91%.
This question belongs to:
Maths
Time and Work
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