Question 73

A can do a piece of work in 6 days. B can do it in 9 days. With the assistance of C they completed the work in 3 days. In how many days can C alone do the work ?

Solution

Let the total work be 18 units.

($$\because$$ LCM of 6, 9 and 3 is 18.)

Efficiency of A = work/time = 18/6 = 3 units/day

Efficiency of B = 18/9 = 2 units/day

Efficiency of (A + B + C) = 18/3 = 6 units/day

Efficiency of C = Efficiency of (A + B + C) - Efficiency of A - Efficiency of B = 6 - 3 - 2 = 1 unit/day

Time taken by C to complete work alone = 18/1 = 18 days

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