day 1 - 20 women working - 1/20th of the work is done.

day 2 - 19W & 1M = 19/400+1/200 = 21/400

day 3 - 18W,1M & 1B = 18/400+1/200+1/800 = 41/800

day 4 - 17W,2M & 1B = 17/400+2/200+1/800 = 43/800

Since on alternate days men and boys are added, there is a similar sequence here.

Writing the above terms in common denominator (800);

40/800 + 42/800 + 41/800 + 43/800 + ......... = 1


We know it will take less than 20 days as the fraction keeps increasing.

Edited

I agree with Vivian, it should be 18 days. (solved it using AP for alternate terms)


Pretty sure this would not be be a GMAT problem, too many calculations

I would agree that this is outside the scope of GMAT. Just by counting, however, I got 18 days, since 17 would not be enough to "complete."