The maturity values of an amount in 5 and 6 years at 8 % simple interest p.a. are Rs.1120 and Rs.1184 respectively. Fmd the amount.

Options

A. Rs . 560
B. Rs. 800
C. Rs. 160
D. Rs. 600

Answer

To solve the problem, we need to find the principal amount (P) based on the given maturity values at 5 and 6 years with an interest rate of 8% per annum.

### Step-by-Step Solution:

1. **Identify the Maturity Values**:
- Maturity value after 5 years (M5) = Rs. 1120
- Maturity value after 6 years (M6) = Rs. 1184

2. **Calculate the Interest for 1 Year**:
- The difference in maturity values between 6 years and 5 years gives us the interest for 1 year.
- Interest for 1 year = M6 - M5 = 1184 - 1120 = Rs. 64

3. **Use the Simple Interest Formula**:
- The formula for simple interest is:
\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]
- Here, the interest for 1 year is Rs. 64, the rate is 8% (or 0.08), and the time is 1 year.
- Therefore, we can set up the equation:
\[ 64 = P \times \frac{8}{100} \times 1 \]

4. **Solve for Principal (P)**:
- Rearranging the equation gives:
\[ P = \frac{64 \times 100}{8} \]
- Simplifying this:
\[ P = \frac{6400}{8} = 800 \]

5. **Conclusion**:
- The principal amount (P) is Rs. 800.

### Final Answer:
The amount (Principal) is Rs. 800.