- If 5 men or 9 women can do a piece of work in 19 days.

- The days required by 3 men and 6 women to do the same work can be figure out in this way.

## Explanation

Two given entities here are

- Men and Women
- Days

To determine the relation here, let suppose; The days required by 3 men and 6 women to do the same work = y

__Case I__

5 men = 9 women

1 man = 9/5 women

3 men = 27/5 women

This clearly indicates that 9 women do the same work as 5 men and 27/5 women do the same wok as 3 men.

When units of given quantities are different we need to change them accordingly.

3 men and 6 women = (27/5 + 6) women

3 men and 6 women = (27 + 30)/5 women

3 men and 6 women = 57/5 women

__Case II__

Women Days

9 19

57/5 y

- More women mean less days.
- Less women mean more days.

This clearly indicates that there is inverse relation.

Direct/Indirect relation tells how the equation will be written.

9 : 57/5 :: y : 19 ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 15)

## To Find

The days required by 3 men and 6 women to do the same work = ?

## Solution

__Method I__

Let suppose

The days required by 3 men and 6 women to do the same work = y

Women Days

9 19

57/5 y

- Relation between women and days is inverse so;

9 : 57/5 :: y : 19

57/5 x y = 9 x 19

57y/5 = 171

57y = 171 x 5

57y = 855

y = 855/57

y = 15 days

**The days required by 3 men and 6 women to do the same work**** = 15 days answer**

__Method II__

5 men = 9 women

1 man = 9/5 women

3 men = 27/5 women

And

3 men and 6 women = (27/5 + 6) women

3 men and 6 women = (27 + 30)/5 women

3 men and 6 women = 57/5 women

The days required by 9 women to do the same work = 19 days

The days required by 1 woman to do the same work = (19 x 9) days

The days required by 1 woman to do the same work = 171 days

The days required by 57/5 women to do the same work = (171 x 5)/57 days

The days required by 57/5 women to do the same work = 15 days

**The days required by 3 men and 6 women to do the same work**** = 15 days answer**

### Conclusion

If 5 men or 9 women can do a piece of work in 19 days, then 15 days would be required by 3 men and 6 women do the same work.