Question 73

A, B and C can individually complete a task in 24 days,16 days and 32 days respectively. If A and C start the work and worked for 6 days and left, then the number of days required by B to complete the remaining task, is:

Solution

Let the total work be 96 units.

($$\because$$ LCM of 24, 16 and 32 is 96.)

Efficiency of A = work/time = 96/24 = 4

Efficiency of B = 96/16 = 6

Efficiency of C = 96/32 = 3

Efficiency of A and C = 4 + 3 = 7

Work done by A and C in 6 days = 7 $$\times$$ 6 = 42 units

Remaining work = 96 - 42 = 54 units

Time taken by B to complete 54 units work = 54/6 = 9 days

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