A can do a piece of work in 4 hours; B and C together can do it in 3 hours, whil

Question

A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

Options:

A . 8 hours

B . 10 hours

C . 12 hours

D . 24 hours

Answer: Option C

A's 1 hour's work = \(\frac{1}{4}\) ,

(B + C)'s 1 hour's work = \(\frac{1}{3}\) ,

(A + C)'s 1 hour's work = \(\frac{1}{2}\) ,

(A + B + C)'s 1 hour's work = \(\left(\frac{1}{4}+\frac{1}{3}\right)=\frac{7}{12}.\)

B's 1 hour's work = \(\left(\frac{7}{12}-\frac{1}{2}\right)=\frac{1}{12}.\)

So, B alone will take 12 hours to do the work.

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