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?

Answer: Option C

$$\frac{250}{100}A\to 15\text{ days}$$
A → 60 days. (Whole work)
Let A do 60 work in 60 days.
A do 15 day work, remaining work completed by A in 45 days. But B do in 30 days.
∴ 45A = 30B
$$\frac{\text{A}}{\text{B}}=\frac{2}{3}\left(\text{efficiency}\right)$$
A + B = 5
Total work = A × 60 = 2 × 60 = 120
50% of 120 = 60
A + B = $$\frac{60}{5}$$ = 12