- A garrison of 500 men had provisions for 27 days.

- After 3 days a reinforcement of 300 men arrived.

- Total days the remaining food would last can be figure out in this way.

## Explanation

Two given entities here are

- Men
- Days

To determine the relation here, let suppose; total days the remaining food would last = y

__Case__

500 men had provisions for 24 days.

After 3 days a reinforcement of 300 men arrived so total men = 500 + 300 = 800 men

Men Days

500 24

800 y

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

This clearly indicates that there is inverse relation.

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

500 : 800 :: y : 24 ________ (i)

800 x y = 500 x 24 ________ (A)

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

## To Find

Total days the remaining food would last = ?

## Solution

__Method I__

Let suppose

Total days the remaining food would last = y

Men Days

500 24

800 y

- Relation between men and days is inverse.

So

500 : 800 :: y : 24

800 x y = 500 x 24

800 x y = 12000

800y = 12000

y = 12000/800

y = 120/8

y = 15

**Total days the remaining food would last = 15 days**

__Method II__

Total provisions = 500 x 27

Total provisions = 13500

3 days provisions = 500 x 3

3 days provisions = 1500

Remaining provisions = 13500 – 1500

Remaining provisions = 12000

After 3 days 300 men join the camp

Total men = 500 + 300

Remaining men = 800 men

Total days the food would last = 12000/800

Total days the food would last = 15 days

**Total days the food would last = 15 days**

## Conclusion

A garrison of 500 men had provisions for 27 days. After 3 days a reinforcement of 300 men arrived. The remaining food would last for 15 days.