Question

Two taps A and B can together fill a swimming pool in 15 days. The taps A and B are kept open for 12 days and then the tap B is closed. It took another 8 days for tap A to fill the pool. How many days does each tap require to fill the pool?​

Answer 1

Let the total capacity of the swimming pool be 120 units. (L.C.M. of 15,12 and 8)
A+B fills a swimming pool in 15 days
Therefore in 1 day A+B fills= 120/15 units= 8 units
Therefore,
in 12 days it fills 12x8 units= 96 units
No of units left to be filled = (120-96)units= 24 units
Tap A fills 24 units in 8 days,
Therefore in one day A fills 3 units.
Therefore A takes, 120/3 days to fill the swimming pool= 40 days.
A+B fills 8 units a day in which A fills up 3 units.
Therefore B fills up (8-3) units a day= 5 units
Therefore B alone will take, (120/5) days = 24 days