Question

Two taps 'A' and 'B' fill a swimming pool in 15 days. Taps 'A' and 'B' are kept open for 12 days and then tap 'B' is closed. It takes another 8 days for the swimming pool to be filled. How many days each tap required to fill the swimming pool?

Answer 1

let the fully filled swimming pool is S.

Two taps A and B fill the swimming pool in 15 days

⇒ A and B fill the swimming pool of S/15 in one day

⇒ A + B = S/15

Given that A and B are kept open for 12 days

if A and B continuously fill the pool for 12 days then the fill 12 × S/15 of the pool

⇒ A and B fill 4S/5 of the pool

⇒ remaining pool to filled is S - 4S/5 = S/5

S/5 of the pool is filled by A in 8 days

⇒ A fills S/40 of the pool in one day

⇒ A fills the entire pool S in 40 days

A fills S/40 of the pool in one day

⇒ B fills S/15 - S/40 of the pool in one day

⇒ B fills 5S/120 of the pool in one day

⇒ B fills S/24 of the pool in one day

⇒ B fills the entire pool S in 24 days

so A tap takes 40 days and B tap takes 24 days to fill the entire pool.