# 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...

+1 vote
61 views

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?

posted May 2, 2018

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.

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

Similar Puzzles
+1 vote

If 15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take, if 3 women do as much work as 2 men?

Six men do a piece of work in 10 days with an effort of 6 hours per day. How many extra men are required for doing the work of double strength in 4 days with an effort of 5 hours per day

+1 vote

P can do a work in 12 days. Q can do the same work in 8 days and R can do the same in 6 days. Q and R start the work and leave after 2 days. P finishes the remaining work in X days. What is the value of 1.1X?

+1 vote

Aadesh alone can do a piece of work in 6 days and Bhavesh alone in 8 days. Aadesh and Bhavesh undertook to do it for Rs. 3200. With the help of Chetan, they completed the work in 3 days.

How much is to be paid to Chetan?

+1 vote

If A men working A hours a day can do A units of a work in A days, then how many units of work can be completed by B men working B hours per day.