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?

+1 vote

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?

0 votes

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.**

0 votes

**3.75 days**

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

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