A alone can do a work in 14 days, whereas B alone can do it in 21 days. B works alone on day 1 while A works alone on day 2, and the process continues, till the work is completed. How many days in all does it take for the work to be completed?

Correct option is B

Given:

A can complete the work in 14 days.

B can complete the work in 21 days.

B works alone on day 1, A works alone on day 2, and this process continues alternately until the work is completed.

Solution:

Let the total work be the LCM of 14 and 21, which is 42 units.

A's one day work = $$\frac{42}{14}$$​= 3 units

B's one day work =$$\frac{42}{21}$$​= 2 units

In two days, the work done is 3 + 2 = 5 units.

In 16 days (8 cycles of 2 days), the work done is 5 $$\times$$​ 8 = 40 units.

On the 17th day, B works and does 2 units of work.

Total work done = 40 + 2 = 42 units.

Therefore, the total number of days taken to complete the work is 17 days.