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??
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
