13. a and b can do a piece of work in 12 days, and b and c can do it in 15 days. if all three of them work together, it can be finished in 10 days. how long will it take for a and c to do it together?
Answers
A and B can do the work in 12 days
⇒ 1 day = 1/12 of the work
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B and C can the work in 15 days
⇒ 1 day = 1/15 of the work
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Find the amount of work A + 2B + C can do in a day:
A + 2B + C = 1/12 + 1/15 = 3/20
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A and B and C can do the work in 10 days:
⇒ 1 day = 1/10 of the work
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Find the amount of work 2A + 2B + 2C can do 1 day:
1 day = 1/10 x 2 = 1/5 of the work
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Find the amount of work A and C can do in a day:
1/5 - 3/20 = 1/20 of the work
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Find the number of days for A and C to complete the work:
1/20 of the work = 1 day
20/20 of the work = 1 x 20 = 20 days
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Answer: A and C need 20 days to complete the work
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