- 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

22.5Â Â Â Â Â Â Â Â Â Â Â 21

21Â Â Â Â Â Â Â Â Â Â Â 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

8Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 21

6Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 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

22.5Â Â Â Â Â Â Â Â Â Â Â 8Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 21

21Â Â Â Â Â Â Â Â Â Â Â Â 6Â Â Â Â Â Â Â Â Â Â Â Â Â 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.