A can complete 25% of a work in 15 days. He works for 15 days and then B alone finishes the remaining work in 30 days. In how many days will A and B working together finish 50% of the same work?

12

A = 25% of work = 15 days,

B = 75% of work = 40 days,

Simplifying, A = \(\frac{1}{4}\)work = 15 days

                  B = \(\frac{3}{4}\)work = 30 days, 

Solving it, we get, A = 60 days, B = 40 days

⇒ Time taken by both of them to complete 50% of the work = 50% of 120 = 60 units.

⇒ \(\frac{60}{2+3}\) = 12 days.