Question 63

A, B and C can individually complete a task in 20 days, 16 days and 30 days, respectively. If A and B started working on the task, and they worked for 4 days and left, then the number of days required by C to finish the remaining task is:

Solution

Let the total work be 240 units.

(LCM of 20, 16 and 30 is 240.)

Efficiency of A = total work/time taken to complete work = 240/20 = 12

Efficiency of B = 240/16 = 15

Efficiency of C = 240/30 = 8

Work done by A and B in 4 days = 4 $$\times (12 + 15) = 4 \times$$ 27 = 108 units

Remaining work = 240 -108 = 132 units

Time taken by C to complete remaining work = 132/8 = 16 $$\frac{4}{8}$$ = 16 $$\frac{1}{2}$$

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