The interest on Rs 750 for 2 year is same as true discount on Rs 960 due 2 year hence if the rate of interest is same in both cases it is.

Options

A. `13%`
B. `12%`
C. `14%`
D. `11%`

Answer

To solve the problem step by step, we need to find the rate of interest where the simple interest on Rs. 750 for 2 years is equal to the true discount on Rs. 960 due in 2 years.

### Step 1: Understand the relationship between Simple Interest and True Discount
The problem states that the simple interest (SI) on Rs. 750 for 2 years is equal to the true discount (TD) on Rs. 960 due in 2 years.

### Step 2: Calculate the True Discount
The true discount can be calculated using the formula:
\[ \text{True Discount} = \text{Present Value} \times \frac{\text{Rate} \times \text{Time}}{100 + \text{Rate} \times \text{Time}} \]
Where:
- Present Value (PV) = Rs. 750
- Future Value (FV) = Rs. 960
- Time (T) = 2 years

### Step 3: Set up the equation for Simple Interest
The simple interest (SI) can be calculated using the formula:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- Principal (P) = Rs. 750
- Rate (R) = Unknown
- Time (T) = 2 years

### Step 4: Equate SI and TD
Since SI = TD, we can write:
\[ \frac{750 \times R \times 2}{100} = \text{True Discount} \]

### Step 5: Calculate the True Discount using the Future Value
The true discount can also be calculated as:
\[ \text{TD} = FV - PV = 960 - 750 = 210 \]

### Step 6: Substitute TD in the equation
Now we can substitute the true discount value into the equation:
\[ \frac{750 \times R \times 2}{100} = 210 \]

### Step 7: Solve for R
1. Multiply both sides by 100:
\[ 750 \times R \times 2 = 21000 \]
2. Divide both sides by 1500 (which is 750 * 2):
\[ R = \frac{21000}{1500} \]
3. Calculate R:
\[ R = 14 \]

### Conclusion
The rate of interest is 14%.