The true discount on a bill of Rs.3720 due after 4 months is Rs. 120. Find the banker's discount -----

Options

A. Rs. 122
B. Rs. 134
C. Rs.124
D. None of these

Answer

To solve the problem of finding the banker's discount on a bill of Rs. 3720 due after 4 months with a true discount of Rs. 120, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **True Discount (TD)**: The difference between the present value and the amount due.
- **Banker's Discount (BD)**: The interest on the amount due for the time period until the bill is due.

2. **Identify Given Values**:
- Amount (A) = Rs. 3720
- True Discount (TD) = Rs. 120
- Time (T) = 4 months

3. **Use the Relationship Between True Discount and Banker's Discount**:
The relationship can be expressed as:
\[ A = BD - TD \]
Rearranging gives:
\[ BD = A + TD \]

4. **Substitute the Known Values**:
Substitute the values into the equation:
\[ BD = 3720 + 120 \]

5. **Calculate Banker's Discount**:
\[ BD = 3840 \]

6. **Final Result**:
The Banker's Discount is Rs. 3840.

### Summary of Steps:
1. Understand the definitions of True Discount and Banker's Discount.
2. Identify the given values (Amount, True Discount, Time).
3. Use the relationship between True Discount and Banker's Discount.
4. Substitute the known values into the equation.
5. Calculate the Banker's Discount.
6. Present the final result.