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?
Let the total work be 36 units.
($$\because$$ LCM of 9, 12 and 18 is 36.)
Efficiency of Amit and Sunil = work/time = 36/9 = 4 units/day
Efficiency of Sunil and Dinesh = 36/12 = 3 units/day
Efficiency of Amit and Dinesh = 36/18 = 2 units/day
Efficiency of Amit, Sunil and Dinesh = $$\frac{4 + 3 + 2}{2}$$ = 9/2
Time taken by Amit, Sunil and Dinesh to complete the work = $$\frac{36}{9/2}$$ = 8 days
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