In a fort,120 men had provisions for 30 days,For how many days is the food sufficient for 100 men?

Answer

To solve the problem step by step, we can use the concept of the Unitary Method.

### Step 1: Calculate the total provisions in man-days.
First, we need to find out the total amount of provisions available in terms of man-days. This is calculated by multiplying the number of men by the number of days they can be sustained.

\[ \text{Total provisions} = \text{Number of men} \times \text{Number of days} \]
\[ \text{Total provisions} = 120 \text{ men} \times 30 \text{ days} = 3600 \text{ man-days} \]

### Step 2: Determine how many days the provisions will last for 100 men.
Now that we know the total provisions available, we can find out how many days these provisions will last for 100 men. We can do this by dividing the total provisions by the number of men.

\[ \text{Number of days} = \frac{\text{Total provisions}}{\text{Number of men}} \]
\[ \text{Number of days} = \frac{3600 \text{ man-days}}{100 \text{ men}} = 36 \text{ days} \]

### Conclusion:
The provisions will last for **36 days** for 100 men.

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