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Q.

A, Band C can do work separately in 16, 32 and 48 days respectively. They started the work together but B leaving off 8 days and C six days before the completion of the work. In what time is the work finished?

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a

12 days

b

10 days

c

14 days

d

9 days

answer is A.

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Detailed Solution

Let work be completed in x days

$ATQ$

$\begin{aligned} \frac{x}{76} + \frac{x - 8}{32} + \frac{x - 6}{48} = 1 \\ x + \frac{x - 8}{2} + \frac{x - 6}{3} = 16 \end{aligned}$

By solving $x = 12$ days

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A, Band C can do work separately in 16, 32 and 48 days respectively. They started the work together but B leaving off 8 days and C six days before the completion of the work. In what time is the work finished?