To do a certain work, efficiencies of A and B are in the ratio 7:5. Working together, they can complete the work in $$17\frac{1}{2}$$ days. In how many days, will B alone complete 50% of the same work?

Let the total work = 700 units

Efficiencies of A and B are in the ratio 7:5.

Let the efficiency of A and B are 7p and 5p respectively.

Efficiencies of A and B together = 7p + 5p = 12p units/day

Working together, they can complete the work in $$17\frac{1}{2}$$ days.

$$\frac{700}{12p}$$ = $$17\frac{1}{2}$$

$$\frac{700}{12p}$$ = $$\frac{35}{2}$$

p = $$\frac{10}{3}$$

Efficiency of B = 5p = $$\frac{50}{3}$$ units/day

Number of days required for B alone complete 50% of the same work = $$\frac{350}{\frac{50}{3}}$$

= $$\frac{350\times3}{50}$$

= 21 days

Hence, the correct answer is Option B