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A can do a piece of work in 30 days and B can do the same piece of work in 20 days. They start working together and work for 4 days and then both leave the work. C alone finishes the remaining work in 18 days. In how many days will C alone finish the whole work?

A can do a piece of work in 30 days and B can do the same piece of work in 20 days. They start working together and work for 4 days and then both leave the work. C alone finishes the remaining work in 18 days. In how many days will C alone finish the whole work? Correct Answer 27

Work done by A in 1 day = 1/30

Work done by B in 1 day = 1/20

⇒ Work done by A and B in 1 day = 1/30 + 1/20 = (2 + 3)/60 = 5/60

⇒ Work done by both in 4 days = 4 × (5/60) = 20/60

C completes 1-20/60 of work = 40/60 of work in 18 days

⇒ 2/3 of work in 18 days

⇒ 1 unit of work in (18)/(2/3) = 27

∴ C can finish the complete work in 27 days.

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