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QA, B, and C can each complete a task in different amounts of time. A and B can do it in 12 days, B and C can do it in 15 days, and C and A can do it in 20 days. How long will it take them to complete the task if they work together, and how long would it take A to complete the task on their own ?
ID: #4619
Time and Work
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#4619Q ID
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Time and WorkTopic
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Correct Answer: Option A
Explanation
(A+B)'s 1 day work = 1/12,
(B+C)'s 1 day work = 1/15,
(C+A)'S 1 day work = 1/20
Including: 2(A+B+C)'s 1 day work = (1/12+ 1/15+ 1/20)= 12/60 = 1/5
∴ (A+B+C) `s 1 day work = (1/2 *1/5) = 1/10
∴ working together they can complete the work in 10 days.
A's 1 day work = (1/10-1/15) = 1/30, B`s 1 day work = (1/10-1/20) = 1/20
C's 1 day work = (1/10-1/12) = 1/60
∴ A alone can take the necessary steps in 30 days
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