Two pipes P and Q can fill a cistern in 10 and 15 minutes respectively. Both are opened together, but at the end of 2 minutes the first is turned off. How many more minutes will it take for the cistern to fill after the first pipe is turned off?  Choose one:  A) 6  B) 7  C) 8  D) 9  E) 10

Rationale: "let x be the total time it takes for the cistern to fill . 2 / 10 + x / 15 = 1 x / 15 = 4 / 5 x = 12 after the first pipe is turned off , it takes 10 more minutes to fill the cistern . the answer is e ."
Answer: E