A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the

Question

A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:

Options:

A . 5 days

B . 6 days

C . 10 days

D . \(10\frac{1}{2}days\)

Answer: Option C

(B + C)'s 1 day's work = \(\left(\frac{1}{9}+\frac{1}{12}\right)=\frac{7}{36} \)

Work done by B and C in 3 days = \(\left(\frac{7}{36}\times3\right)=\frac{7}{12} \)

Remaining work = \(\left(1-\frac{7}{12}\right)= \frac{5}{12}\)

Now, \(\frac{1}{24} \) work is done by A in 1 day.

So, \(\frac{5}{12}\) work is done by A in \(\left(24\times\frac{5}{12}\right)= 10 days.\)

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