A and B working alone can finish a task in 12 and 16 days respectively. In how many days can the task be finished if they work for one day each alternatively, and A begins the work?

Correct option is D

Given:

Number of days taken by A to complete a work = 12

Number of days taken by B to complete a work = 16

Formula used:

Find the efficiency of the person

work = efficiency × time

Solution:

Total work (L.C.M of 12 and 16) = 48 units

Work done by A in one day = $$\frac{48}{12}$$​

=> 4 units

Work done by B in one day = $$\frac{48}{16}$$​

=> 3 units

Work done by A and B in two days (when work alternatively) = 4 units + 3 units

=> 7 units

work done by A and B in 12 days = 7 × 6

=> 42 units

work done on 13th day = 42 + 4

=> 46 units

Remaining work = (48 - 46) units

= 2 units

work done by B of 2 units = $$\frac{2}3$$​ days

Total time taken by A and B when work alternatively is $$13\frac{2}{3}$$ days.

Thus, correct answer is option (d).