A can complete a work in 16 days and B in 20 days. If both work together, 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 and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete it?
Correct Answer: Option D
Explanation:
Combined 1-day work = 1/4. A's 1-day work = 1/12. B's 1-day work = 1/4 - 1/12 = 2/12 = 1/6. Therefore, B alone can complete the work in 6 days.
Combined 1-day work = 1/4. A's 1-day work = 1/12. B's 1-day work = 1/4 - 1/12 = 2/12 = 1/6. Therefore, B alone can complete the work in 6 days.
This question belongs to:
Maths
Time and Work
Question #2
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A can build a wall in 15 days, and B can destroy it in 20 days. If they work on alternate days starting with A, in how many days will the wall be built?
Correct Answer: Option D
Explanation:
Total work = LCM(15, 20) = 60 units. Efficiency of A = +4, B = -3. In 2 days (A then B), net work done = 4 - 3 = 1 unit. We need to reach 60 - 4 = 56 units first. 56 units will be done in 56 * 2 = 112 days. On the 113th day, A works and completes 4 units, making the total work 56 + 4 = 60 units. So, the wall is completed in 113 days.
Total work = LCM(15, 20) = 60 units. Efficiency of A = +4, B = -3. In 2 days (A then B), net work done = 4 - 3 = 1 unit. We need to reach 60 - 4 = 56 units first. 56 units will be done in 56 * 2 = 112 days. On the 113th day, A works and completes 4 units, making the total work 56 + 4 = 60 units. So, the wall is completed in 113 days.
This question belongs to:
Maths
Time and Work
Question #3
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A can complete a work in 32 days and B in 19 days. If both work together, in how many days will the work be completed?
Correct Answer: Option B
Explanation:
Combined rate = 1/32 + 1/19. Time = 11.92 days.
Combined rate = 1/32 + 1/19. Time = 11.92 days.
This question belongs to:
Maths
Time and Work
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