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

Answer: Option C

$$\begin{array}{rl}& \text{A’s 1 hour’s work}=\frac{1}{4}\\ & \left(\text{B}+\text{C}\right)\text{’s 1 hour’s work}=\frac{1}{3}\\ & \left(\text{A}+\text{C}\right)\text{’s 1 hour’s work}=\frac{1}{2}\\ & \left(\text{A}+\text{B}+\text{C}\right)\text{’s 1 hour’s work}\\ & =\frac{1}{4}+\frac{1}{3}\\ & =\frac{7}{12}\\ & \therefore \text{B’s 1 hour’s work}\end{array}$$
= (A + B + C)'s 1 hour's work - (A + C)'s 1 hour's work
$$\begin{array}{rl}& =\frac{7}{12}-\frac{1}{2}\\ & =\frac{1}{12}\end{array}$$
So, B alone can complete the work in 12 hours.