ii) Two taps A and B can together 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 pool
to be filled. How many days does each tap
require to fill the pool?
(HOTS)
Answers
Question:-
Two taps A and B can together 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 pool to be filled. How many days does each tap require to fill the pool?
Answer:-
➵ Time taken by (A + B) to fill the pool = 15 days
➵ Work done by (A + B) in 1 day = 1/15
A and B both are opened for 12 days:-
➵ Work done by (A + B) in 12 days = 12 * (1/15) = 12/15
B is closed (Only A works):-
➵ Remaining work to be done by A = 1 - 12/15 = 3/15 = 1/5
➵ Time taken by A to do the remaining work (1/5) = 8 days
➵ Work done by A in 1 day = 1/(5*8) = 1/40
➵ Time taken by A to do full work ( 1 ) = 40 days
➵ Work done by (A + B) in 1 day = 1/15
➵ Work done by A in 1 day + Work done by B in 1 day = 1/15
➵ 1/40 + Work done by B in 1 days = 1/15
➵ Work done by B in 1 day = 1/15 - 1/40 = (40 - 15)/600
➵ Work done by B in 1 day = 1/24
➵ Time taken by B to do full work ( 1 ) = 24 days.