A can complete a work in 12 days and B in 25 days. If they work together, the work will be completed in: MCQ with Answer and Explanation
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Question #1
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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 can A and B together complete the work?
Correct Answer: Option D
Explanation:
Let total work be 80 units. Efficiency of A = 1 unit/day. In 10 days, A completes 10 units. Remaining work = 80 - 10 = 70 units. B finishes 70 units in 42 days, so B's efficiency = 70 / 42 = 5/3 units/day. Combined efficiency of A and B = 1 + 5/3 = 8/3 units/day. Time taken together = 80 / (8/3) = (80 * 3) / 8 = 30 days.
Let total work be 80 units. Efficiency of A = 1 unit/day. In 10 days, A completes 10 units. Remaining work = 80 - 10 = 70 units. B finishes 70 units in 42 days, so B's efficiency = 70 / 42 = 5/3 units/day. Combined efficiency of A and B = 1 + 5/3 = 8/3 units/day. Time taken together = 80 / (8/3) = (80 * 3) / 8 = 30 days.
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Maths
Time and Work
Question #2
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A can complete a work in 13 days and B can complete the same work in 28 days. If they work together, in how many days will the work be completed?
Correct Answer: Option C
Explanation:
Combined rate = 1/13 + 1/28. Time = 1 รท combined rate = 8.88 days.
Combined rate = 1/13 + 1/28. Time = 1 รท combined rate = 8.88 days.
This question belongs to:
Maths
Time and Work
Question #3
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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 D
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.
This question belongs to:
Maths
Time and Work
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