Question : A can complete a piece of work in 14 days, while A and B together can complete it in $3\frac{1}{2}$ days. How long will B alone take to complete it?
Option 1: $4$ days
Option 2: $5$ days
Option 3: $\frac{3}{14}$ days
Option 4: $\frac{14}{3}$ days
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Correct Answer: $\frac{14}{3}$ days
Solution :
A alone can do the work in 14 days.
So, the one day's work of A = $\frac{1}{14}$
A and B together can complete a work in $3 \frac{1}{2} = \frac{7}{2}$
Combined one day's work of A and B = $\frac{2}{7}$
Thus, the one day's work of B = The one day's work of both A and B – One day's work of A
$= \frac{2}{7} - \frac{1}{14}$
$= \frac{4-1}{14} = \frac{3}{14}$
$\therefore$ Time taken by B alone = $\frac{1}{\text{One day's work of B}}=\frac{1}{\frac{3}{14}} = \frac{14}{3}$ days
Hence, the correct answer is $\frac{14}{3}$ days.
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