2000 soldiers in a fort had enough food for 20 days. But some soldiers were transferred to another fort and the food lasted for 25 days. How many soldiers were transferred ?

Options

A. 400
B. 450
C. 525
D. 500

Answer

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

### Step 1: Understand the initial conditions
We know that:
- There are 2000 soldiers.
- The food lasts for 20 days for these soldiers.

### Step 2: Calculate the total amount of food in soldier-days
The total amount of food can be calculated as:
\[ \text{Total food} = \text{Number of soldiers} \times \text{Number of days} = 2000 \text{ soldiers} \times 20 \text{ days} = 40000 \text{ soldier-days} \]

### Step 3: Set up the new conditions after some soldiers are transferred
Let \( X \) be the number of soldiers transferred. Therefore, the number of soldiers remaining in the fort is:
\[ 2000 - X \]
The food now lasts for 25 days for the remaining soldiers.

### Step 4: Calculate the new total amount of food in soldier-days
The total amount of food for the remaining soldiers can also be expressed as:
\[ \text{Total food} = \text{Remaining soldiers} \times \text{New number of days} = (2000 - X) \times 25 \]

### Step 5: Set the equations equal to each other
Since the total amount of food remains the same, we can set the two expressions for total food equal to each other:
\[ 40000 = (2000 - X) \times 25 \]

### Step 6: Solve for \( X \)
First, simplify the equation:
\[ 40000 = 2000 \times 25 - X \times 25 \]
\[ 40000 = 50000 - 25X \]
Now, rearranging gives:
\[ 25X = 50000 - 40000 \]
\[ 25X = 10000 \]
Dividing both sides by 25:
\[ X = \frac{10000}{25} = 400 \]

### Conclusion
The number of soldiers transferred is:
\[ \boxed{400} \]

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