On what sum of money will the difference between S.I and C.I for 2 years at `5%` per annum be equal to Rs 25?

Options

A. Rs 10,000
B. Rs, 10,500
C. Rs 9,500
D. Rs 9000

Answer

To find the sum of money (principal) on which the difference between Simple Interest (S.I) and Compound Interest (C.I) for 2 years at a rate of 5% per annum is equal to Rs 25, we can use the formula for the difference between S.I and C.I for 2 years:

\[ \text{Difference} = \frac{P \times r^2}{100^2} \]

where:
- \( P \) = Principal amount (the sum of money we need to find)
- \( r \) = Rate of interest (5% in this case)

Given that the difference is Rs 25, we can set up the equation:

\[ 25 = \frac{P \times 5^2}{100^2} \]

Now, let's solve for \( P \):

### Step 1: Substitute the values into the equation
Substituting \( r = 5 \):

\[ 25 = \frac{P \times 25}{10000} \]

### Step 2: Simplify the equation
Multiply both sides by 10000 to eliminate the fraction:

\[ 25 \times 10000 = P \times 25 \]

### Step 3: Calculate the left side
Calculating the left side:

\[ 250000 = P \times 25 \]

### Step 4: Isolate \( P \)
Now, divide both sides by 25 to solve for \( P \):

\[ P = \frac{250000}{25} \]

### Step 5: Perform the division
Calculating the division:

\[ P = 10000 \]

Thus, the sum of money (principal) is Rs 10,000.

### Final Answer:
The principal amount is Rs 10,000.

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