Pipe P alone can fill up a cistern in 15 hours. Pipe Q alone can fill the same cistern in 20 hours. The pipes are simultaneously opened and it is found that due to a leakage at the bottom of the cistern, it takes 60/91 hours extra for the cistern to be completely filled. Calculate the time taken by the leak to empty the completely filled up cistern if both the pipes are closed.

Pipe P fills in 15 hours, so rate = 1/15 per hour. Pipe Q fills in 20 hours, so rate = 1/20 per hour. Combined rate of P+Q = 1/15 + 1/20 = 7/60 per hour. Normal time to fill = 60/7 hours. With leak, time = 60/7 + 60/91 = (60×13)/91 = 780/91 hours. Actual fill rate = 91/780 per hour. Leak rate = (7/60) - (91/780) = (91-91)/780 = 0. Wait, let me recalculate: Combined rate of P+Q = 7/60. With leak, effective rate = 1/(60/7 + 60/91) = 1/((60×13 + 60)/91) = 91/(60×14) = 91/840. Leak rate = 7/60 - 91/840 = 98/840 - 91/840 = 7/840 = 1/120. So leak empties full tank in 120 hours. Option C is correct.