A B and C can do a piece of work in 12 18 and 24 days respectively They all begin together A work c...........

Quant (SSC) Time and work

A, B and C can do a piece of work in 12, 18 and 24 days, respectively. They all begin together. A work continuously till it is finished, B leaves the work 2 days before its completion and C leaves the work 4 days before its completion. In what approximate time is the work finished?

4 days

7 days

5 days

9 days

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Explanation:

Let the work is finished in x days
Work done by A in 1 day = 1/12
Work done by B in 1 day = 1/18
Work done by C in 1 day = 1/24
x /12 + x - 2 /18 + x - 4 /24 = 1
⇒ x/12 + x/18 - x/18 + x/24 - 4/24 = 1
⇒ x/12 + x/18 + x/24 = 1 + 1/9 + 1/6
⇒ 6x + 4x +3x /72
= 18 + 2 + 3 /18
⇒ 13x /72 = 23/18
⇒ x = 7.07 ≈ 7 days