Pipes A and B can fill a tank in 12 minutes and 15 minutes, respectively. The tank when full can be emptied by pipe C in x minutes. When all the three pipes are opened simultaneously, the tank is full in 10 minutes. The value of x is:

Pipes A and B fill at rates 1/12 and 1/15 per minute respectively. Together they fill at 1/12 + 1/15 = 9/60 = 3/20 per minute. Pipe C empties at 1/x per minute. Net rate with all three = 3/20 - 1/x = 1/10 (since tank fills in 10 minutes). Solving: 3/20 - 1/10 = 1/x, so 1/x = 1/20, giving x = 20 minutes. The emptying pipe partially offsets the filling pipes.