Pipe A alone can fill a tank in 8 hours. Pipe B alone can fill it in 6 hours. If both the pipes are opened and after 2 hours pipe A is closed, then the other pipe will fill the tank in

Part of the tank filled by both pipes in two hours $=2left(frac{1}{8}+frac{1}{6} ight)=2left(frac{3+4}{24} ight)=frac{7}{12}$ Remaining part $=1-frac{7}{12}=frac{5}{12}$ Time taken by B in filling the remaining part $=frac{5}{12} imes 6=frac{5}{2}=2 frac{1}{2}$ hours Alternative:

( Total work = Time × Efficiency)

Pipe A and B filled the tank in 2 hours

= (3 + 4) × 2 = 14 units

Time taken by pipe B to fill the remaining part

$=frac{24-14}{4}=frac{10}{4}$ hours $=2 frac{1}{2}$ hours