Question

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

Answer 1

Let a women alone can do a work in x days

Let a man alone do a work in y days

In a day, They can do 1/x, 1/y part of work respectively.

Given,

4 men and 6 men can complete a work in 8 days.

In one day,

They can complete 1/8th work

Equation for this,

4(1/y)+6(1/x) = 1/8 [Let 1/y = v, 1/x = u]

4v + 6u = 1/8

Also,

3 men and 7 women can complete in 10 days.

In a day, They complete 1/10th work

Equation for this,

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

3v + 7u = 1/10

Solving both equations ;

12v + 18u = 3/8 - - - - - ( Equation 1) × 3

12v + 28u = 4/10 - - - - ( Equation 2)×4

10u = 4/10 - 3/8 = 16/40-15/40

10u = 1/40

u = 1/400

We don't calculate " v" because we don't need it.

So, u = 1/x

1/x = 1/400

x = 400 days.

Therefore, a women can complete a work in 400 days.

Now, A women does 1/400th part of work each day.

If ten women work each day, They do 10/400 = 1/40th part of work each day.

Number of days taken by ten women = 1 ÷ 1/40 = 40.

Therefore, 10 women can complete the work in 40 days!