- 15 men take 21 days of 8 hours each to do a piece of work.
- 3 women do as much work as 2 men.
- Days required by the 21 women if each works for 6 hours can be figure out in this way.
Explanation
Three given entities here are
- Women
- Hours
- Days
To determine the relation here, let suppose; Days required by the 21 women if each works for 6 hours = y
Case I
As
2 men = 3 women
1 men = 3/2 women
15 men = (3 x 15)/2
15 men = 45/2
15 men = 22.5 women
Women Days
22.5 21
21 y
- More women mean less days.
- Less women mean more days.
This clearly indicates that there is direct relation.
Direct/Indirect relation tells how the equation will be written.
21 : 22.5 :: 21 : y ________ (i)
Case II
Hours Days
8 21
6 y
- More hours mean less days.
- Less hours mean more days.
This clearly indicates that there is inverse relation.
Direct/Indirect relation tells how the equation will be written.
6 : 8 :: 21 : y ________ (ii)
By (i) and (ii)
21 : 22.5 :: 21 : y
6 : 8
21 x 6 x y = 22.5 x 8 x 21 ________ (A)
After simplifying equation (A), we can easily figure out the value of y (y = 30 days)
To Find
Days required by the 21 women if each works for 6 hours = ?
Solution
Method I
Let suppose
Days required by the 21 women if each works for 6 hours = y
Women Hours Days
22.5 8 21
21 6 y
- Relation between women and days is inverse.
- Relation between hours and days is also inverse.
So
21 : 22.5 :: 21 : y
6 : 8
21 x 6 x y = 22.5 x 8 x 21
126y = 3780
y = 3780/126
y = 30 days
Days required by the 21 women if each works for 6 hours = 30 days
Method II
As
2 men = 3 women
1 men = 3/2 women
15 men = (3 x 15)/2
15 men = 45/2
15 men = 22.5 women
Days required by the 22.5 women if each works for 8 hours = 21 days
Days required by the 22.5 women if each works for 1 hour = (21 x 8) days
Days required by the 22.5 women if each works for 1 hour = 168 days
Days required by the 1 woman if she works for 1 hour = (168 x 22.5) days
Days required by the 1 woman if she works for 1 hour = 3780 days
Days required by the 21 woman if each works for 1 hour = 3780/21 days
Days required by the 21 woman if each works for 1 hour = 180 days
Days required by the 21 woman if each works for 6 hours = 180/6 days
Days required by the 21 woman if each works for 6 hours = 30 days
Days required by the 21 women if each works for 6 hours = 30 days
Conclusion
15 men take 21 days of 8 hours each to do a piece of work. 30 days of 6 hours each would 21 women take if 3 women do as much work ass 2 men.
