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 ?

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