A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?

$$\eqalign{ & {\text{Part}}\,{\text{filled}}\,{\text{by}}\,(A + B)\,{\text{in}}\,{\text{1}}\,{\text{minute}} \cr & = {\frac{1}{{60}} + \frac{1}{{40}}} = \frac{1}{{24}} \cr & {\text{Suppose}}\,{\text{the}}\,{\text{tank}}\,{\text{is}}\,{\text{filled}}\,{\text{in}}\,x\,{\text{minutes}} \cr & {\text{Then}},\,\frac{x}{2}\left( {\frac{1}{{24}} + \frac{1}{{40}}} \right) = 1 \cr & \Rightarrow \frac{x}{2} \times \frac{1}{{15}} = 1 \cr & \Rightarrow x = 30\,\text{minutes} \cr} $$