- 12 men working 8 hours per day complete a piece of work in 18 days.

- Hours in a day for 15 men to complete the same work in 12 days can be figure out in this way.

## Explanation

Three given entities here are

- Men
- Days
- Hours

To determine the relation here, let suppose; Hours in a day for 15 men to complete the same work in 12 days = y

__Case I__

Men Hours

12 8

15 y

- Lesser men mean more hours in a day are required to finish the job.
- More men mean less hours in a day to finish the given job.

This clearly indicates that there is inverse relation.

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

12 : 15 :: y : 8 ________ (i)

__Case II__

Days Hours

18 8

12 y

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

This clearly indicates that there is inverse relation.

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

18 : 12 :: y : 8 ________ (ii)

By (i) and (ii)

12 : 15 :: y : 8

18 : 12

12 x 18 x 8 = 15 x 12 x y ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 9.6 hours)

## To Find

Hours in a day for 15 men to complete the same work in 12 days = ?

## Solution

__Method I__

Let suppose

Hours in a day for 15 men to complete the same work in 12 days = y

Men Days Hours

12 18 8

15 12 y

- Relation between men and hours is inverse.
- Relation between days and hours is also inverse so;

12 : 15 :: y : 8

18 : 12

12 x 18 x 8 = 15 x 12 x y

1728 = 180y

1728/180 = y

y = 9.6

**Hours in a day for 15 men to complete the same work in 12 days**** = 9.6 hours answer**

__Method II__

Hours in 18 day for 12 men to complete the work = 8 hours

Hours in 18 days for 1 man to complete the work = (8 x 12) hours

Hours in a day for 1 man to complete the work = (8 x 12 x 18) hours

Hours in 12 days for 1 man to complete the work = (8 x 12 x 18)/12 hours

Hours in 12 days for 15 men to complete the work = (8 x 12 x 18)/(12 x 15) hours

Hours in 12 days for 15 men to complete the work = 1728/180 hours

Hours in 12 days for 15 men to complete the work = 9.6 hours

**Hours in a day for 15 men to complete the same work in 12 days**** = 9.6 hours answer**

### Conclusion

12 men working 8 hours per day complete a piece of work in 18 days. 9.6 hours a day must 15 men work to complete the same work in 12 days.