If Manohar pays an interest of RS. 750 for 2 years on a sum of Rs. 4500, find the rate of interest

Question

Accepted Answer

To determine the rate of interest, we can use the formula for simple interest:

$$ \text{Simple Interest (SI)} = \frac{\text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)}}{100} $$

Given:
- Simple Interest (SI) = Rs. 750
- Principal (P) = Rs. 4500
- Time (T) = 2 years

We need to find the Rate (R).

Substituting the given values into the formula:

$$ 750 = \frac{4500 \times R \times 2}{100} $$

Simplifying the equation:

$$ 750 = \frac{9000R}{100} $$

$$ 750 = 90R $$

Now, solve for R:

$$ R = \frac{750}{90} $$

$$ R = 8.3333\% $$

This is equivalent to $ 8\frac{1}{3}\% $, which matches Option 2.

**Explanation for why Option 2 is correct:**
- The calculation shows that the rate of interest is $ 8\frac{1}{3}\% $, which is exactly what Option 2 states. Therefore, Option 2 is the correct answer.

**Explanation for why the other options are incorrect:**
1. **Option 1 (0.08):** This option suggests a rate of 8%, which is not the same as $ 8\frac{1}{3}\% $. The calculated rate is slightly higher than 8%, making this option incorrect.
   
2. **Option 3 (0.09):** This option suggests a rate of 9%, which is higher than the calculated rate of $ 8\frac{1}{3}\% $. Therefore, this option is incorrect.

3. **Option 4 (9$\frac{2}{3}%$):** This option suggests a rate of $ 9\frac{2}{3}\% $, which is significantly higher than the calculated rate of $ 8\frac{1}{3}\% $. Thus, this option is incorrect.

In conclusion, the correct rate of interest is $ 8\frac{1}{3}\% $, which is accurately represented by Option 2.