What sum of money will amount to Rs. 520 in 5 years and to Rs. 568 in 7 years at simple interest?

Options

A. Rs. 400
B. Rs. 120
C. Rs. 510
D. Rs. 220

Answer

To solve the problem, we need to determine the principal amount (the initial sum of money) that will amount to Rs. 520 in 5 years and Rs. 568 in 7 years under simple interest.

### Step-by-Step Solution:

1. **Identify the Amounts and Time Periods**:
- Amount after 5 years (A1) = Rs. 520
- Amount after 7 years (A2) = Rs. 568
- Time for A1 = 5 years
- Time for A2 = 7 years

2. **Calculate the Interest Earned in 2 Years**:
- The interest earned from year 5 to year 7 is:
\[ \text{Interest for 2 years} = A2 - A1 = 568 - 520 = Rs. 48 \]

3. **Calculate the Interest Earned in 1 Year**:
- Since the interest is earned uniformly over the years, the interest for 1 year is:
\[ \text{Interest for 1 year} = \frac{48}{2} = Rs. 24 \]

4. **Calculate the Total Interest for 5 Years**:
- The total interest earned over 5 years is:
\[ \text{Total Interest for 5 years} = 5 \times \text{Interest for 1 year} = 5 \times 24 = Rs. 120 \]

5. **Determine the Principal Amount**:
- The principal amount (P) can be found using the formula for the amount in simple interest:
\[ A = P + \text{Total Interest} \]
- Rearranging gives us:
\[ P = A - \text{Total Interest} \]
- Substituting the values for A (after 5 years):
\[ P = 520 - 120 = Rs. 400 \]

### Final Answer:
The sum of money (principal amount) is Rs. 400.