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?

A completes 25% work in 15 days, so total work for A = 60 days. A's rate = 1/60 per day. A works for 15 days, completing 15/60 = 1/4 of work. Remaining work = 3/4. B completes 3/4 work in 30 days, so B's rate = (3/4)/30 = 1/40 per day. Combined rate of A + B = 1/60 + 1/40 = 5/240 = 1/24 per day. For 50% (1/2) of work: time = (1/2)/(1/24) = 12 days, matching option D.