6 men & 8 women can do a work in 10 days, 4 men & 7 women can do it in 12 days, how many days will 4 men and 12 women...

Question

If 6 men and 8 women can do a piece of work in 10 days and 4 men and 7 women can do it in 12 days, how many days will 4 men and 12 women take to do half of work?

Answer 1

6 men and 8 women = 1 work in 10 days = 1/10 ------ 1
4 men and 7 women = 1 work in 12 days = 1/12 ------- 2

2 * 8/7
32/7 men + 8 women = 2/21 ----- 3

3 - 1
(32/7 - 6)men = 2/21 - 1/10
(-10/7)men = -1/210
men = (1/210)*(7/10) = (1/300) ------ 4

Sub 4 in 1
(6/300) + 8 women = 1/10
8 women = 1/10 - 1/50 = 4/50
women = (1/100) ----------- 5

4 men and 12 women = 4*(1/300) + 12*(1/100) = 1/75 + 12/100 = 2/15 = 2 work in 15 days or 1/2 work in 3.75 days.

Answer 2

3.75 days

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Let the work be =1, man's work for one day =m, woman's work for one day =w and x= the number of days required for 4 men +12 woman to complete work, then we have:
1) 6m+8w=1/10
2) 4m+7w=1/12
3) 4m+12w=1/x

From 1) and 2) we find that
60m+80w=1=48m+84w->
12m=4w->3m=w,
then m=1/300, w=1/100
Now lets find x,
x=1/(4m+12w)=1/(4/300+12/100)=1/(40/300)=300/40=7.5
x= 7.5 days
x/2 for half a work=7.5/2=3.75 days