3 men and 7 women can do a job in 5 days while 4 men and 6 women's can do it in 4 dyas the number of days required for a group of 10 women working together at the same rate as before to finish the same job

Let 1 Man complete the job in x days and 1 woman complete the job in y days
Now, 1 Man's 1 day work =1/x and 1 woman's 1 day work=1/y
3 men and 7 women 's 1 day work will be
3/x+7/y =1/5( they complete work in 5 days, so in 1 day their work will be 1/5) (1)
similarly 4 men and 6 women's 1 day work will be 4/x+6/y=1/4
Taking 1/x=u and 1/y=v and solving
3u+7v=1/5
4u+6v=1/4
we get v=1/200
So y=200
so this means 1 woman takes 200 days to complete the job
Now 10 women will take 200/10= 20 days