Pipe A and Q can fill a tank in 15 hrs and 20 hrs respectively. Pipe A is opened for two third of the time and then both pipes are opened for the remaining time. How long will it take to fill the tank?

12 hrs

ATQ,

Let total time taken to fill the tank is 't' hours.

Then,

⇒ [4 × \(\frac{2t}{3}\)] + [7 × \(\frac{t}{3}\)] = 60

⇒ [\(\frac{8}{3}\) + \(\frac{7}{3}\)] t = 60

⇒ 5 t = 60

⇒ t = \(\frac{60}{5}\) = 12 hrs.