Question

4 men and 6 women can complete a work in 8 days while 3 men and 7 women can completed it in 10days in how many days will 10 women complete it

Answer 1

Let m be a man's one day effort and w be a woman's one day effort.

4m+6y=1/8
3m+7y=1/10
10y=1/?? => ??=1/10y

12m+18y=3/8
12m+28y=4/10
=> 10y = 4/10-3/8 => 10y = 1/40

Hence ?? = 40 days.

Answer 2

Let the work done by 1 men in 1-day be x.

Let the work done by 1 women in 1-day be y.

Given,

 4x + 6y = 1/8  ----- (1)

3x + 7y = 1/10 ----- (2)


On solving (1) * 3 & (2) * 4, we get

12x + 28y = 4/10

12x + 18y = 3/8

-----------------------

         10y = 1/40

            y = 1/400.


Now,

We got 1 women's 1-day work = 1/400.

Then 10-women's 1-day work = 1/400 * 10

                                                  = 1/40.


Therefore 10 women can complete the work in 40 days.


Hope this helps!