A fort has food stock for 220 soldiers. If a soldier get 45 gram per day then the stock can last for 16 weeks. Then how many soldiers should left the fort so that food would last for 24 weeks when daily intake of food per soldier is reduced to 33 gram per day?

Options

A. 44
B. 160
C. 20
D. 52

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the total food stock available
The food stock is sufficient for 220 soldiers for 16 weeks, with each soldier receiving 45 grams of food per day.

- **Total food stock** = Number of soldiers × Daily food per soldier × Number of days
- Number of days in 16 weeks = 16 weeks × 7 days/week = 112 days
- Total food stock = 220 soldiers × 45 grams/soldier/day × 112 days

**Calculation**:
\[ \text{Total food stock} = 220 \times 45 \times 112 = 1,098,000 \text{ grams} \]

### Step 2: Set up the equation for the new scenario
Now, we want to find out how many soldiers should leave the fort so that the remaining food lasts for 24 weeks with a reduced daily intake of 33 grams per soldier.

- Number of days in 24 weeks = 24 weeks × 7 days/week = 168 days
- Let the number of remaining soldiers be \( X \).
- Total food consumed in the new scenario = Remaining soldiers × Daily food per soldier × Number of days
- Total food consumed = \( X \times 33 \times 168 \)

### Step 3: Set the total food stock equal to the food consumed in the new scenario
Since the total food stock remains the same, we can set up the equation:
\[ 1,098,000 = X \times 33 \times 168 \]

### Step 4: Solve for \( X \)
Now, we can solve for \( X \):
\[ X = \frac{1,098,000}{33 \times 168} \]

**Calculation**:
\[ X = \frac{1,098,000}{5,544} \approx 198 \]

### Step 5: Calculate how many soldiers should leave
Initially, there were 220 soldiers. The number of soldiers that should leave is:
\[ \text{Soldiers left} = 220 - X = 220 - 198 = 22 \]

### Conclusion
Thus, **22 soldiers should leave the fort** to ensure that the food lasts for 24 weeks with a daily intake of 33 grams per soldier.