A can complete a work in 19 days and B in 22 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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X can do a piece of work in 40 days. He works at it for 8 days and then Y alone finishes the remaining work in 16 days. How long will X and Y together take to complete the work?
Correct Answer: Option C
Explanation:
Let total work be 40 units. Efficiency of X = 1 unit/day. In 8 days, X completes 8 units. Remaining work = 40 - 8 = 32 units. Y finishes 32 units in 16 days, so Y's efficiency = 32 / 16 = 2 units/day. Combined efficiency of X and Y = 1 + 2 = 3 units/day. Time taken together = 40 / 3 = 13(1/3) days.
Let total work be 40 units. Efficiency of X = 1 unit/day. In 8 days, X completes 8 units. Remaining work = 40 - 8 = 32 units. Y finishes 32 units in 16 days, so Y's efficiency = 32 / 16 = 2 units/day. Combined efficiency of X and Y = 1 + 2 = 3 units/day. Time taken together = 40 / 3 = 13(1/3) days.
This question belongs to:
Maths
Time and Work
Question #2
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Two workers A and B are engaged to do a piece of work. Working together they would take 8 hours less than the time taken by A alone, and 4.5 hours less than the time taken by B alone. Find the time they take to complete the work together.
Correct Answer: Option B
Explanation:
Let the time taken together be t hours. Then A takes (t + 8) hours and B takes (t + 4.5) hours. Using the direct formula for such problems: t = sqrt(a * b), where a and b are the extra times. t = sqrt(8 * 4.5) = sqrt(36) = 6 hours.
Let the time taken together be t hours. Then A takes (t + 8) hours and B takes (t + 4.5) hours. Using the direct formula for such problems: t = sqrt(a * b), where a and b are the extra times. t = sqrt(8 * 4.5) = sqrt(36) = 6 hours.
This question belongs to:
Maths
Time and Work
Question #3
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A can complete a work in 14 days and B can complete the same work in 19 days. If they work together, in how many days will the work be completed?
Correct Answer: Option A
Explanation:
Combined rate = 1/14 + 1/19. Time = 1 รท combined rate = 8.06 days.
Combined rate = 1/14 + 1/19. Time = 1 รท combined rate = 8.06 days.
This question belongs to:
Maths
Time and Work
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