A and B working together can fill an empty cistern in 8 hours. A alone can fill \(\frac{5}{4}\) part of the tank in 20 hrs. Find the time taken by B alone to fill three fourth of the tank.

8 h

\(\frac{5}{4}\)th of the tank filled by A in = 20 hrs.

⇒ Full tank filled by A in = \(\frac{20 × 4 }{5}\) = 16 hrs

⇒ A and B together can fill it in = 8 hrs.

Therefore,

B alone fills it in = \(\frac{16}{1}\) = 16 hrs

\(\frac{3}{4}\) of the tank filled by B in = 16 × \(\frac{3}{4}\) = 12 hours