Labour and work problem - 20 women replaced by a men and boy alternatively

Problem:

20 women can finish a job in 20 days. After each day, one woman is replaced by a man or a boy alternatively starting with a man. Man is twice efficient and boy is half efficient as a woman. On which day does the job get completed?

Solution:

Lets treat man as 2 women and boy as half woman. Starting 1st day 1 W is removed and 1M added. So, we have 21W at work. Next day, 1B is added and 1W is removed, so, we have 20.5 W now.

Now add there units of work daily, and check if it is just greater than 400, because total unit of work is 20X20 = 400.

So, each alternative day when man is added, we do following unit of work
21,21.5,22 and so on. So, an AP with d=0.5, a = 21

Similarly for alternative day when a boy is added we have following unit of work:
20.5,21,21.5 and so on.

Now, by hit and trial, we get 9 days of man add and 9 days of boy add and total is 18 days.

Answer :

                18 days