Question : A and B together can do a piece of work in 6 days and A alone can do it in 9 days. The number of days B will take to do it alone is:
Option 1: 18 days
Option 2: 24 days
Option 3: 9 days
Option 4: 12 days
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Correct Answer: 18 days
Solution : A and B together can do a piece of work in 6 days. So in 1 day, they can do $\frac{1}{6}$th part of the work. Also A alone can do it in 9 days. ⇒ In 1 day he alone can do $\frac{1}{9}$ part of the work. ⇒ B alone in 1 day can do $(\frac{1}{6}-\frac{1}{9}) = (\frac{3-2}{18}) = \frac{1}{18}$th part of the work $\therefore$ The number of days B will take to do it alone is = $(\frac{1}{\frac{1}{18}}$) = 18 days Hence, the correct answer is 18 days.
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