A sum of money, invested at 7.5% simple interest p.a. became Rs. 689 on maturity after 4 years. What was the original sum invested?

Options

A. Rs.560
B. Rs.520
C. Rs.530
D. Rs.540

Answer

To find the original sum invested (the principal amount), we can use the formula for simple interest and the information given in the problem.

### Step-by-Step Solution:

1. **Identify the Variables:**
- Let the original sum invested be \( P \) (the principal).
- The rate of interest \( R = 7.5\% \) per annum.
- The time \( T = 4 \) years.
- The total amount after 4 years \( A = Rs. 689 \).

2. **Use the Simple Interest Formula:**
The formula for the amount in simple interest is:
\[ A = P + SI \]
where \( SI \) (Simple Interest) is given by:
\[ SI = \frac{P \times R \times T}{100} \]

3. **Substituting the Values:**
Substitute the values into the formula:
\[ A = P + \frac{P \times 7.5 \times 4}{100} \]
This simplifies to:
\[ 689 = P + \frac{30P}{100} \]
\[ 689 = P + 0.3P \]
\[ 689 = 1.3P \]

4. **Solve for \( P \):**
Now, we can solve for \( P \):
\[ P = \frac{689}{1.3} \]

5. **Calculating \( P \):**
To perform the division:
\[ P = \frac{6890}{13} \quad (\text{Multiplying numerator and denominator by 10}) \]
Now, divide \( 6890 \) by \( 13 \):
\[ P = 530 \]

6. **Conclusion:**
The original sum invested is \( Rs. 530 \).

### Final Answer:
The original sum invested was **Rs. 530**.

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