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Amit and Sunil together can complete a work in 9 days, Sunil and Dinesh together can complete the same work in 12 days, and Amit and Dinesh together can complete the same work in 18 days. In how many days will they complete the work if Amit, Sunil and Dinesh work together?

Amit and Sunil together can complete a work in 9 days, Sunil and Dinesh together can complete the same work in 12 days, and Amit and Dinesh together can complete the same work in 18 days. In how many days will they complete the work if Amit, Sunil and Dinesh work together? Correct Answer 8 days

A = Amit, S = Sunil and D = Dinesh

Total work = LCM of (9, 12 and 18) = 36

Hence, efficiency of A + S = 4

Efficiency of S + D = 3

Efficiency of A + D = 2

Now, Efficiency of A + S + D = (4 + 3 + 2)/2 = 9/2

∴ A, S and D together work in = 36/(9/2) = 4 × 2 = 8 days

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