A and B working together can do 30% of the work in 6 days. B alone can do the same work in 25 days. How long will A alone take to complete the same work?

Given, A and B working together can do 30% of the work in 6 days

$$\Rightarrow$$ A and B working together can do 10% of the work in 2 days

$$\Rightarrow$$ A and B working together can do 100% of the work in 20 days

Let the total work = W

Work done by A and B together in 1 day = $$\frac{W}{20}$$

B alone can do the same work in 25 days

Work done by B alone in 1 day = $$\frac{W}{25}$$

$$\Rightarrow$$ Work done by A alone in 1 day = $$\frac{W}{20}-\frac{W}{25}=\frac{5W-4W}{100}=\frac{W}{100}$$

$$\therefore\ $$Number of days required for A alone to complete the work = 100 days

Hence, the correct answer is Option A