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?

$$\frac{{250}}{{100}}A \to 15{\text{ days}}$$
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