Problema Solution
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 requires to fill the swimming pool?
Answer provided by our tutors
Time taken by 'A' and 'B' together to fill the tank = 15 days
Work done by 'A' and 'B' in 1 day = 1/15
Work done by 'A' and 'B' in 12 days working together = 1/15*12 = 4/5
Work left = 1-4/5 = 1/5
Work done in 8 days by 'A' = 1/5
=> Work done by 'A' in one day = 1/5*1/8 = 1/40
=> Time taken by 'A' to compelte the work = 1/(1/40) = 40 days
Work done by 'A' alone in 15 days = 1/40 * 15 = 3/8
Work done by 'B' alone in 15 days = 1 - work done by 'A' = 1 - 3/8 = 5/8
=> work done by 'B' alone in 1 day = 5/8 *1/15 = 1/24
=> time taken by 'B' alone to finish the work = 24 days