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
Answers
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!