2 man and 3 women can do a piece of work in 10 days while 3 man and 2 women can do the same work in 8 days. In how many days can 2 man and 4 women do the work?

According to the question :

( 2m + 3w )10d = ( 3m + 2w )8d

20m + 30w = 24m + 16w

30w - 16w = 24m - 20m

14w = 4m

3.5w = 1 m

Now put the 1 man work in first equation .

work = ( 2m + 3w )10d

( 7w + 3w )10d

( 10w )10d

100w d

work = 100w d / 2m + 4w

work = 100w d / 7w + 4w

work = 100w d / 11w

work = 100/11 d

work = 100 / 11

100 / 11 days can 2 man and 4 women do the work