Question

Two taps A and B can together fill the 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 pool to be filled. How many days does each tap require to fill the pool?

Answer 1

AMOUNT OF WORK DONE BY A+B IN 15 DAYS= 1 PART
AMOUNT OF WORK DONE IN 1 DAY = 1/15 PART.
THEREFORE, AMOUNT OF WORK DONE IN 12 DAYS = 1/15*12 = 4/5
THEREFORE,WORK LEFT = 1- 4/5
= 1/5
TAP B IS CLOSED
THEREFORE,
TIME REQUIRED FOR DOING 1/5 WORK FOR A = 8 DAYS. (GIVEN)
TIME REQUIRED BY A FOR DOING 1 WORK = 8 ÷ 1/5
=40 DAYS.

A+B= 1/15 WORK PER DAY
A = 1/40 WORK PER DAY
THERFORE,
B = 1/15 - 1/40
= 1/24 WORK PER DAY
THERFORE ,B WILL TAKE 24 DAYS TO FILL THE POOL ALONE.
A WILL TAKE 40 DAYS TO FILL THE POOL ALONE.