An inlet pipe P can fill a tank in x minutes, while an outlet pipe Q can empty the fully filled tank in (x − 5) minutes. If both pipes are opened together, they can empty a fully filled tank in 60 minutes. Find the time taken by pipe P alone to completely fill the tank.

ATQ, Let the capacity of the tank be 1 unit. Rate of P (inlet) = 1/x tank per minute Rate of Q (outlet) = 1/(x − 5) tank per minute Since the tank is getting emptied when both are open: Net emptying rate = (outflow − inflow) = 1/(x − 5) − 1/x Given that they empty the tank in 60 minutes: 1/(x − 5) − 1/x = 1/60 Compute the left side: ( x − (x − 5) ) / [x(x − 5)] = 1/60 5 / [x(x − 5)] = 1/60 So, x(x − 5) = 5 × 60 x(x − 5) = 300 x² − 5x − 300 = 0 Factor: (x − 20)(x + 15) = 0 So x = 20 or x = −15. Time cannot be negative, so: x = 20.