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P can do a piece of work in 20 days and Q can do the same piece of work in 30 days. They start working together and work for 5 days and then both leave the work. R alone finishes the remaining work in 21 days. In how many days will R alone finish the whole work?

P can do a piece of work in 20 days and Q can do the same piece of work in 30 days. They start working together and work for 5 days and then both leave the work. R alone finishes the remaining work in 21 days. In how many days will R alone finish the whole work? Correct Answer 36

P can do a piece of work in 20 days

Part of work P can do in a day = 1/20

Q can do a piece of work in 30 days.

Part of work Q can do in a day = 1/30

∴ Part of work P and Q can do in 5 days together = 5/20 + 5/30 = 5/12

∴ Remaining part of work = 1 - (5/12) = 7/12

R finishes 7/12th part of the work in 21 days

∴ R can complete the whole work alone in 21/(7/12) = 36 days

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