The true discount on Rs. 2575 due 4 months hence is Rs. 75. The rate per cent is-

Options

A. `6%`
B. `8%`
C. `9%`
D. `5%`

Answer

To find the rate percent based on the true discount, we can follow these steps:

### Step 1: Identify the Given Values
- True Discount (TD) = Rs. 75
- Amount (A) = Rs. 2575
- Time (T) = 4 months

### Step 2: Calculate Present Value (PV)
The Present Value (PV) can be calculated using the formula:
\[ PV = A - TD \]
Substituting the given values:
\[ PV = 2575 - 75 = 2500 \]

### Step 3: Convert Time into Years
Since the time is given in months, we need to convert it into years:
\[ T = \frac{4}{12} = \frac{1}{3} \text{ years} \]

### Step 4: Use the Formula for Rate of True Discount
The formula for the rate of true discount is:
\[ R = \frac{100 \times TD}{PV \times T} \]
Substituting the values we have:
\[ R = \frac{100 \times 75}{2500 \times \frac{1}{3}} \]

### Step 5: Simplify the Calculation
Calculating the denominator:
\[ PV \times T = 2500 \times \frac{1}{3} = \frac{2500}{3} \]
Now substituting back into the rate formula:
\[ R = \frac{100 \times 75}{\frac{2500}{3}} \]
This simplifies to:
\[ R = \frac{100 \times 75 \times 3}{2500} \]

### Step 6: Further Simplify
Calculating the numerator:
\[ 100 \times 75 \times 3 = 22500 \]
Now we have:
\[ R = \frac{22500}{2500} \]
This simplifies to:
\[ R = 9\% \]

### Conclusion
The rate percent is **9%**.

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