A invests Rs. 2500 for 2 years at 11% per annum on simple interest and B invests the same money, for the same time and at 10% per annum on compound interest then find the difference between both the interests.

Options

A. Rs 25
B. Rs 27
C. Rs 30
D. Rs 50

Answer

To solve the problem step by step, we will calculate the simple interest earned by A and the compound interest earned by B, and then find the difference between the two.

### Step 1: Calculate Simple Interest for A
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(P\) = Principal amount = Rs. 2500
- \(R\) = Rate of interest = 11%
- \(T\) = Time period = 2 years

Substituting the values into the formula:
\[ SI = \frac{2500 \times 11 \times 2}{100} \]
Calculating:
\[ SI = \frac{2500 \times 22}{100} = \frac{55000}{100} = 550 \]

### Step 2: Calculate Compound Interest for B
The formula for the amount (A) in compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \(P\) = Principal amount = Rs. 2500
- \(R\) = Rate of interest = 10%
- \(T\) = Time period = 2 years

Substituting the values into the formula:
\[ A = 2500 \left(1 + \frac{10}{100}\right)^2 \]
Calculating:
\[ A = 2500 \left(1 + 0.1\right)^2 = 2500 \left(1.1\right)^2 \]
\[ A = 2500 \times 1.21 = 3025 \]

Now, to find the compound interest (CI):
\[ CI = A - P = 3025 - 2500 = 525 \]

### Step 3: Find the Difference Between Both Interests
Now, we find the difference between the simple interest earned by A and the compound interest earned by B:
\[ \text{Difference} = SI_A - CI_B = 550 - 525 = 25 \]

### Final Answer
The difference between both the interests is Rs. 25.

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