Solution:
Concept- 40,24 days each tap will take to fill the pool respectively.To solve this question, we need to know the basics of time and work. Let us assume that tap A works at the rate of A job/day and that tap B works at the rate of B job/day.
Using these assumptions, we will form two equations with two variables selected already, A and B, as per the two conditions provided in the question and solve those equations to obtain our desired answer.
Given in question statement that, A and B can together fill a swimming pool in 15 days, i.e., 15A + 15B = 1 (job)…(i) [1 Job refers to completing 1 job]
Also given in question that, A and B are kept open for 12 days and then closing tap B, it takes another 8 days for the pool to be filled by tap A alone, i.e.,
20A + 12B = 1 (job)…(ii)
Dividing (i) by 3 on both sides, we get,
...(iii)And dividing (ii) by 4 on both sides, we get,
...(iv)Comparing equations (iii) and (iv), we get,
(Job/Day)That is, B can complete
Job in 1 day,Then, B can complete 1 Job in
days.From equation 3, we know that,
i.e., A can do 
(job/day).Then, A can complete 1 job in
days.Hence, the correct answer is 40 & 24 days.
