Question

2 women and 5 women can together finish an embroidery work in 4 days while 3 women and 6 men can finish the same work in 3 days find the time taken by 1 men alone is a work and also the time taken by one man alone

Answer 1

Let time taken by one woman = x days
Let time taken by one man = y days

Work done by women in 1 day = 1/x
Work done by a man in 1 day = 1/y

It is given: 2 women and 5 men can finish work in 4 days.
A.T.Q

4(2/x + 5/y) = 1
Also, 3(3/x + 6/y) = 1/3 (From second case)
Put 1/x = u anf 1/y = v

Then equations will be:
2u + 5v = 1/4
3u +6v = 1/3
By solving these equations by any method (substitution or elimination), we will get:
v = 1/36 and u = 1/18
On comparing,
v = 1/y = 1/36
u = 1/x = 1/18

we will get y = 36 and u = 18