On what sum of money will the difference between S.I and C.I for 2 years at 5% per annum be equal to ₹ 25?
2 वर्ष के लिए 5% प्रतिवर्ष दर से साधारण ब्याज और चक्रवृद्धि ब्याज के बीच अंतर कितनी धन राशि पर ₹25 के बराबर होगा?

Options

A. A)10000
B. B)10.5
C. C)9500
D. D)9000

Explanation

To solve the problem of finding the sum of money on which the difference between Simple Interest (S.I) and Compound Interest (C.I) for 2 years at 5% per annum is equal to ₹25, we can follow these steps:

### Step 1: Understand the formula for the difference between C.I and S.I
The difference between Compound Interest and Simple Interest for 2 years can be calculated using the formula:
\[ \text{Difference} = \frac{R^2}{100^2} \times P \]
where \( R \) is the rate of interest and \( P \) is the principal amount.

### Step 2: Substitute the known values into the formula
In this case, the rate \( R \) is 5% and the difference is ₹25. Therefore, we can substitute these values into the formula:
\[ 25 = \frac{5^2}{100^2} \times P \]

### Step 3: Calculate \( \frac{5^2}{100^2} \)
Calculating \( \frac{5^2}{100^2} \):
\[ \frac{5^2}{100^2} = \frac{25}{10000} = 0.0025 \]

### Step 4: Set up the equation
Now, we can set up the equation using the value we calculated:
\[ 25 = 0.0025 \times P \]

### Step 5: Solve for \( P \)
To find \( P \), we can rearrange the equation:
\[ P = \frac{25}{0.0025} \]
Calculating \( P \):
\[ P = 25 \div 0.0025 = 10000 \]

### Conclusion
The sum of money on which the difference between S.I and C.I for 2 years at 5% per annum is equal to ₹25 is ₹10,000.