John invested a sum of money at an annual simple interset rate of 10%. At the end of four years the amount invested plus interset earned was Rs 770. The amount invested was

Options

A. Rs 650
B. Rs 350
C. Rs 550
D. Rs 500

Answer

To find the amount John invested, we can use the formula for simple interest and the relationship between principal, interest, and total amount.

### Step-by-Step Solution:

1. **Identify the given values:**
- Let \( P \) be the principal amount (the amount invested).
- The rate of interest \( R = 10\% \) per annum.
- The time period \( T = 4 \) years.
- The total amount after 4 years \( A = 770 \) Rs.

2. **Recall the formula for total amount in simple interest:**
\[ A = P + SI \]
where \( SI \) (Simple Interest) can be calculated using the formula:
\[ SI = \frac{P \times R \times T}{100} \]

3. **Substituting the values into the formula:**
\[ A = P + \frac{P \times R \times T}{100} \]
Substituting the known values:
\[ 770 = P + \frac{P \times 10 \times 4}{100} \]

4. **Simplifying the equation:**
\[ 770 = P + \frac{40P}{100} \]
\[ 770 = P + 0.4P \]
\[ 770 = 1.4P \]

5. **Solving for \( P \):**
\[ P = \frac{770}{1.4} \]
\[ P = \frac{7700}{14} \]
\[ P = 550 \]

6. **Conclusion:**
The amount John invested was Rs 550.