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
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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