Two pipes, P ans Q can fill a cistern in 12 and 15 minutes

Two pipes, P ans Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill ?

12(1 - t/25) = 3
∴ t = 45/4 = 11¹/₄ minutes
∴ Required answer = 11¹/₄ - 3
= 8¹/₄ minutes