In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case ?

Options

A. A) 693
B. B) 741
C. C) 528
D. D) 654

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Calculate the total provisions available in the fort.
We know that there are 1200 soldiers, each consuming 3 kg of food per day, and the provisions last for 30 days.

Total provisions = Number of soldiers × Daily consumption per soldier × Number of days
\[ \text{Total provisions} = 1200 \, \text{soldiers} \times 3 \, \text{kg/soldier/day} \times 30 \, \text{days} \]
\[ \text{Total provisions} = 1200 \times 3 \times 30 = 108000 \, \text{kg} \]

### Step 2: Set up the equation for the new scenario.
Now, let \( x \) be the number of additional soldiers joining. The total number of soldiers becomes \( 1200 + x \). Each soldier now consumes 2.5 kg per day, and the provisions last for 25 days.

Total provisions in this scenario can be expressed as:
\[ \text{Total provisions} = (1200 + x) \times 2.5 \, \text{kg/soldier/day} \times 25 \, \text{days} \]

### Step 3: Equate the total provisions from both scenarios.
Since the total provisions remain the same, we can set the two expressions equal to each other:
\[ 108000 = (1200 + x) \times 2.5 \times 25 \]

### Step 4: Simplify the equation.
First, simplify the right side:
\[ (1200 + x) \times 2.5 \times 25 = (1200 + x) \times 62.5 \]

Now, equate:
\[ 108000 = (1200 + x) \times 62.5 \]

### Step 5: Solve for \( x \).
Divide both sides by 62.5:
\[ \frac{108000}{62.5} = 1200 + x \]
\[ 1728 = 1200 + x \]

Now, isolate \( x \):
\[ x = 1728 - 1200 \]
\[ x = 528 \]

### Conclusion:
The number of soldiers joining the fort is \( 528 \).

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