On a certain sum, the compound interest in 2 years amounts to Rs 4,240. If the rates of interest for successive years are 10% and 15% respectively, find the sum.

Answer

To solve the problem step by step, we will use the formula for compound interest and the given information.

### Step-by-Step Solution:

1. **Identify the given values**:
- Compound Interest (CI) for 2 years = Rs 4,240
- Rate of interest for the first year (R1) = 10%
- Rate of interest for the second year (R2) = 15%

2. **Use the formula for Compound Interest**:
The formula for compound interest after 2 years is:
\[ CI = P \left( \left(1 + \frac{R1}{100}\right) \times \left(1 + \frac{R2}{100}\right) - 1 \right) \]
Where:
- \( P \) = Principal amount (the sum we need to find)
- \( R1 \) = Rate of interest for the first year
- \( R2 \) = Rate of interest for the second year

3. **Substitute the values into the formula**:
\[ 4240 = P \left( \left(1 + \frac{10}{100}\right) \times \left(1 + \frac{15}{100}\right) - 1 \right) \]

4. **Calculate the expressions inside the parentheses**:
- First, calculate \( 1 + \frac{10}{100} = 1 + 0.10 = 1.10 \)
- Next, calculate \( 1 + \frac{15}{100} = 1 + 0.15 = 1.15 \)
- Now multiply these two results:
\[ 1.10 \times 1.15 = 1.265 \]
- Now subtract 1 from this result:
\[ 1.265 - 1 = 0.265 \]

5. **Substitute back into the equation**:
\[ 4240 = P \times 0.265 \]

6. **Solve for \( P \)**:
\[ P = \frac{4240}{0.265} \]

7. **Calculate the value of \( P \)**:
- To simplify the division, we can multiply both the numerator and denominator by 1000 to eliminate the decimal:
\[ P = \frac{4240 \times 1000}{265} = \frac{4240000}{265} \]
- Performing the division:
\[ P \approx 16000 \]

### Final Answer:
The sum (Principal amount) is Rs 16,000.

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