A bathtub can be filled by a cold pipe in 15 minutes and by a hot pipe in 10 minutes. A man opens both the taps at 7
a.m. and leaves the bathroom. He returns at the time when the tub was expected to be full, but he observes that the waste pipe in the bottom was open and the tub was not full. He now closes it, and it takes 4 more minutes before the tank is full. After using the bathtub for 10 minutes, he opens the waste pipe. At what time will the tub be empty?

LCM of 15 and 10 = 30  Let the capacity of the tub be 30 liters. The amount of water filled by cold pipe in 1 min = 30 / 15 = 2 liters The amount of water filled by hot pipe in 1 min = 30 / 10 = 3 liters Total amount of water filled in 1 minute = 2 + 3 = 5 litres Time taken to fill the tub = 30 / 5 = 6 minutes The man forgot to close the waste pipe. It takes 4 more minutes to fill the tub after closing the waste pipe. Time taken = 6 + 4 = 10 minutes Let us assume that the waste pipe removes x liters of water in 1 min Amount of water filled when the waste pipe was open = 6 × ( 2 + 3 - x ) = 6 × ( 5 - x )  Amount of water filled when the when the waste water pipe was closed = 4 × ( 2 + 3 ) = 4 × 5 = 20 litres The total amount of water filled =  6 × ( 5 - x ) + 20 = 30 litres LCM of 15 and 10 = 30  Let the capacity of the tub be 30 liters. The amount of water filled by cold pipe in 1 min = 30 / 15 = 2 liters The amount of water filled by hot pipe in 1 min = 30 / 10 = 3 liters Total amount of water filled in 1 minute = 2 + 3 = 5 litres Time taken to fill the tub = 30 / 5 = 6 minutes The man forgot to close the waste pipe. It takes 4 more minutes to fill the tub after closing the waste pipe. Time taken = 6 + 4 = 10 minutes Let us assume that the waste pipe removes x liters of water in 1 min Amount of water filled when the waste pipe was open = 6 × ( 2 + 3 - x ) = 6 × ( 5 - x )  Amount of water filled when the when the waste water pipe was closed = 4 × ( 2 + 3 ) = 4 × 5 = 20 litres The total amount of water filled =  6 × ( 5 - x ) + 20 = 30 litres 30 - 6x + 20 = 30  x = 10 / 3 litres Amount of water removed by waste pipe in 1 min = ( 10 / 3 ) litres Time taken to empty the bathtub = ( 30 / ( 10/3 ) ) = 9 minutes The time when the bathtub will be empty is = Time taken to fill the tub + Time taken by the man to use the tub + Time taken to empty the tub by the waste pipe = 10 min + 10 min + 9 min = 29 minutes So, The bathtub will be empty at 7.29 am