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?

$$\eqalign{ & {\text{A's}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}} = \frac{1}{4}; \cr & {\text{(B + C)'s}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}} = \frac{1}{3}; \cr & {\text{(A + C)'s}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}} = \frac{1}{2}. \cr & {\text{(A + B + C)'s}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}} \cr & = {\frac{1}{4} + \frac{1}{3}} = \frac{7}{{12}} \cr & {\text{B's}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}} \cr & = {\frac{7}{{12}} - \frac{1}{2}} = \frac{1}{{12}} \cr & \therefore {\text{B}}\,{\text{along}}\,{\text{will}}\,{\text{take}}\,{\text{12}}\,{\text{hours}}\,{\text{to}}\,{\text{do}}\,{\text{the}}\,{\text{work}} \cr} $$