A can complete a piece of work in 14 days, while A and B together can complete it in 31/2 days. How long will B alone take to complete it?

A can complete a piece of work in 14 days, while A and B…

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?

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. $\frac{14}{3}$ days.

Time taken by A = 14 days

Time taken by A and B together = $3\frac{1}{2}$ days = $\frac{7}{2}$ = 3.5 days

Let the total work to be done (LCM of 14, $\frac{7}{2}$ ) be 14 units.

Efficiency of A = 14/14 = 1 unit/day

Efficiency of A and B = 14/3.5 = 4 units/day

Now, efficiency of B = 3 units/day

So, Time taken by B alone = 14/3 days