- If 15 men working 9 hours a day can reap a field in 16 days.

- Then the required days in which 18 men reap the field, working 8 hours a day can be figure out in this way.

## Explanation

Three given entities here are

- Men
- Hours
- Days

To determine the relation here, let suppose; days required by the 18 men to reap the field, working 8 hours a day = y

__Case I__

Men Days

15 16

18 y

- Less men means more days required to finish a particular job.
- More men means less days are required to get the job done.

This clearly indicates that there is inverse relation.

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

18 : 15 :: 16 : y ________ (i)

__Case II__

Hours Days

9 16

8 y

- More hours means less days.
- Less days means more hours would be required to get the job done.

This clearly indicates that there is inverse relation.

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

8 : 9 :: 16 : y ________ (ii)

By (i) and (ii)

18 : 15 :: 16 : y

8 : 9

15 x 9 x 16 = 18 x 8 x y ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 49)

## To Find

Days required by the 18 men to reap the field, working 8 hours a day = ?

## Solution

__Method I__

Let suppose

Days required by the 18 men to reap the field, working 8 hours a day = y

Men Hours Days

15 9 16

18 8 y

Relation between men and days & hours and days is inverse so;

18 : 15 :: 16 : y

8 : 9

15 x 9 x 16 = 18 x 8 x y

2160 = 144y

y = 2160/144

y = 15 days

**Days required by the18 men to reap the field, working 8 hours a day = 15 days answer**

__Method II__

Days required by 15 men, working 9 hours a day = 16 days

Days required by 15 men, working 1 hour a day = 16 x 9 days

Days required by 15 men, working 1 hour a day = 144 days

Days required by 1 man, working 1 hour a day = 144 x 15 days

Days required by 1 man, working 1 hour a day = 2160 days

Days required by 18 men, working 1 hour a day = 2160/18 days

Days required by 18 men, working 1 hour a day = 120 days

Days required by 18 men, working 8 hours a day = 120/8 days

Days required by 18 men, working 8 hours a day = 15 days

**Days required by the18 men to reap the field, working 8 hours a day = 15 days answer**

## Conclusion

If 15 men working 9 hours a day can reap a field in 16 days, in 15 days 18 men will reap the field, working 8 hours a day.