The interest on Rs. 750 for 2 years is equal to the true discount on Rs. 810 for the same time and at the same rate. The rate per cent is-

Options

A. `4 1/3 %`
B. `5 1/6 %`
C. `4%`
D. `5%`

Answer

To solve the problem, we need to find the rate of interest given that the interest on Rs. 750 for 2 years is equal to the true discount on Rs. 810 for the same time and at the same rate.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Principal (Present Worth) = Rs. 750
- Amount (Future Value) = Rs. 810
- Time (T) = 2 years

2. **Calculate the Simple Interest (SI):**
The formula for Simple Interest is:
\[ \text{SI} = \text{Principal} \times \text{Rate} \times \text{Time} / 100 \]
We need to express SI in terms of the rate (R):
\[ \text{SI} = 750 \times \frac{R}{100} \times 2 \]
Simplifying this gives:
\[ \text{SI} = 15R \]

3. **Calculate the True Discount (TD):**
The True Discount is calculated as:
\[ \text{TD} = \text{Amount} - \text{Present Worth} = 810 - 750 = 60 \]

4. **Set the Simple Interest equal to the True Discount:**
Since the interest on Rs. 750 for 2 years is equal to the true discount on Rs. 810:
\[ 15R = 60 \]

5. **Solve for R:**
To find R, divide both sides by 15:
\[ R = \frac{60}{15} = 4 \]

6. **Conclusion:**
The rate of interest is 4%.

### Final Answer:
The rate per cent is **4%**.

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