Question
M can do a piece of work in 20 days. He works at it
alone for 5 days and N alone finishes the remaining work in 9 days. In how many days, both of them together can complete the work ?Solution
M finishes the work in 20 days So, work done by M in 1 day = 1/20 Work done by M in 5 days = 1/20 × 5 = 1/4 Remaining work = 1 - (1/4) = 3/4 So, 3/4 work is done by N in 9 days. If the whole work is done by N, 9 × (4/3) = 12 So, work done by N in 1 day = 1/12 (A + B)'s one day of work = (1/20) + (1/12) ⇒ (3 + 5)/60 = 8/60  M and N will both finish work in 60/8 = 7.5 days. ∴ M and N will both finish work in 7.5 days.
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