The true discount on a bill of Rs. 1860 due after 8 months is Rs. 60. Find the banker's gain-----

Options

A. Rs.1.5
B. Rs.2.5
C. Rs.4
D. Rs.2

Answer

To solve the problem, we need to find the banker's gain given the true discount and the amount of the bill. Let's break this down step by step.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Amount of the bill (A) = Rs. 1860
- True Discount (TD) = Rs. 60
- Time (T) = 8 months

2. **Calculate the Present Worth (PW)**:
The Present Worth can be calculated using the formula:
\[ PW = A - TD \]
Substituting the values:
\[ PW = 1860 - 60 = 1800 \]

3. **Calculate the Banker's Gain (BG)**:
The Banker's Gain can be calculated using the formula:
\[ BG = \frac{(TD)^2}{PW} \]
Substituting the values:
\[ BG = \frac{60^2}{1800} \]
Calculating \(60^2\):
\[ 60^2 = 3600 \]
Now substituting back:
\[ BG = \frac{3600}{1800} \]
Simplifying this gives:
\[ BG = 2 \]

4. **Final Answer**:
The Banker's Gain is Rs. 2.