Correct Answer - Option 1 : 29 minutes past 7 a.m.
Given:
Bathtub can be filled by cold pipe in 15 minutes and hot pipe in 10 minutes.
Both pipes opened at 7 am
It takes 4 more minutes to fill the tub after the man returns
He uses the bathtub for 10 minutes
Calculation:
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 literes
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
