A bathtub can be filled by a cold pipe in 15 minutes and

Solution

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