- A fort had provision of food for 150 men for 45 days.

- After 10 days, 25 men left the fort.

- The number of days for which the remaining food will last can be figure out in this way.

## Explanation

Two given entities here are

- Men
- Days

To determine the relation here, let suppose; Number of days for which the remaining food will last = y

__Case__

As we know that;

MenÂ Â Â Â Â Â Â Â Â Â Days

150Â Â Â Â Â Â Â Â Â Â Â Â 35

125Â Â Â Â Â Â Â Â Â Â Â Â y

- Provision of food for days decreases as men increases.
- Provision of food for days increases as men decreases.

This clearly indicates that there is inverse relation.

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

150 : 125 :: y : 35 ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 42)

## To Find

Number of days for which the remaining food will last = ?

## Solution

__Method I__

Let suppose

Number of days for which the remaining food will last = y

MenÂ Â Â Â Â Â Â Â Â Â Days

150Â Â Â Â Â Â Â Â Â Â Â Â 35

125Â Â Â Â Â Â Â Â Â Â Â Â y

Relation between men and days is inverse, so;

150 : 125 :: y : 35

150 x 35 = y x 125

5250 = 125y

5250/125 = y

y = 42

**Number of days for which the remaining food will last = 42 days answer**

__Method II__

150 men had provision of food = 35 days

1 man had provision of food = 35 x 150 days

1 man had provision of food = 5250 days

125 man had provision of food = 5250/125 days

125 man had provision of food = 42 days

**Number of days for which the remaining food will last = 42 days answer**

## Conclusion

A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The remaining food will last for 42 days.