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

A can do a piece of work in 4 hours, B and C can do it in 3 hours. A and C can do it in 2 hours. How long will B alone take to do it?
[A]8 hours
[B]24 hours
[C]10 hours
[D]12 hours

12 hours
A’s one hour’s work $= \frac{1}{4}$
(B + C)’s one hour’s work $= \frac{1}{3}$
(A + C)’s one hour’s work $= \frac{1}{2}$
∴ C’s one hour’s work $= \frac{1}{2}-\frac{1}{4} = \frac{2-1}{4} = \frac{1}{4}$
B’s one hour’s work $= \frac{1}{3}-\frac{1}{4} = \frac{4-3}{12} = \frac{1}{12}$
Hence B alone can do the work in 12 hours, so option [D] is correct answer.