Question

4 women and 6 men can together finished a piece of work in 5 days, while 3 women and 4 men can finis h it in 7 days. Find the time taken by 1 woman alone to finish the work, and that taken by 1 man alone.

Answer 1

Answer:

Let one woman takes X days to finish the work

And one takes Y days to finish the work

According to the question

2/x+5/y =1/4

4(2y+ 5x) = 1xy

8y+20x = xy...(1)

3/x+ 6/y = 1/3

3(3y + 6y) = xy

9y + 18x = xy....(2)

[8y+20x = xy]×9=72y+180x= 9xy

[9y+18x=xy]×8=-72y±144x=8xy

36x= xy

y= 36

8×36+20x=36x

288/16= x

x=18

therefore one women takes 18 days and one man can takes 36 days to finish the work.