The compound interest on a certain sum for 2 years at `10%` per annum is Rs.525. Then simple interest on the same principal for double the time but at half the rate `%`per annum differs by:

Options

A. Rs.25
B. Rs.70
C. Rs.50
D. Rs.120

Answer

To solve the problem step by step, we will follow the outlined process:

### Step 1: Identify the given information
- Compound Interest (CI) for 2 years = Rs. 525
- Rate of interest (R) = 10% per annum
- Time (T) = 2 years

### Step 2: Calculate the Principal (P)
The formula for Compound Interest is:
\[ CI = A - P \]
Where \( A \) is the amount after time \( T \).

The formula for the amount \( A \) in compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]

Substituting the values we have:
\[ A = P \left(1 + \frac{10}{100}\right)^2 \]
\[ A = P \left(1 + 0.1\right)^2 \]
\[ A = P \left(1.1\right)^2 \]
\[ A = P \times 1.21 \]

Now substituting \( A \) in the CI formula:
\[ 525 = P \times 1.21 - P \]
\[ 525 = P(1.21 - 1) \]
\[ 525 = P \times 0.21 \]

Now, solving for \( P \):
\[ P = \frac{525}{0.21} \]
\[ P = 2500 \]

### Step 3: Calculate Simple Interest (SI)
Now we need to find the Simple Interest for double the time (4 years) at half the rate (5% per annum).

The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]

Substituting the values:
- \( P = 2500 \)
- \( R = 5\% \)
- \( T = 4 \)

So,
\[ SI = \frac{2500 \times 5 \times 4}{100} \]
\[ SI = \frac{50000}{100} \]
\[ SI = 500 \]

### Step 4: Find the difference between CI and SI
Now we find the difference between the Compound Interest and Simple Interest:
\[ \text{Difference} = CI - SI \]
\[ \text{Difference} = 525 - 500 \]
\[ \text{Difference} = 25 \]

### Final Answer
The difference between the Compound Interest and Simple Interest is Rs. 25.

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