The banker's discount on a bill due 6 months hence at `6%` is Rs. 37.08 . The true discount is -----

Options

A. Rs.6.18
B. Rs.12.36
C. Rs.48
D. Rs.36

Answer

To find the true discount when given the banker's discount, we can use the formula:

\[ \text{True Discount} = \frac{\text{Banker's Discount} \times 100}{100 + (\text{Rate} \times \text{Time})} \]

### Step-by-Step Solution:

1. **Identify the given values**:
- Banker's Discount (BD) = Rs. 37.08
- Rate (R) = 6%
- Time (T) = 6 months = \( \frac{6}{12} = \frac{1}{2} \) years

2. **Convert the time into years**:
- Since the time is given in months, we convert it to years. 6 months is equal to \( \frac{1}{2} \) years.

3. **Calculate the denominator**:
- The denominator of the formula is \( 100 + (R \times T) \).
- First, calculate \( R \times T \):
\[ R \times T = 6 \times \frac{1}{2} = 3 \]
- Now, add this to 100:
\[ 100 + 3 = 103 \]

4. **Substitute the values into the formula**:
- Now, substitute the Banker's Discount and the calculated denominator into the formula:
\[ \text{True Discount} = \frac{37.08 \times 100}{103} \]

5. **Calculate the True Discount**:
- First, calculate \( 37.08 \times 100 = 3708 \).
- Now divide by 103:
\[ \text{True Discount} = \frac{3708}{103} \approx 36 \]

6. **Final Answer**:
- The True Discount is approximately Rs. 36.

### Summary:
The True Discount is Rs. 36.