The true discount at a bill of X 7440 due 16 months, hence is X 240. Find the banker's gain.

Options

A. 1) 10
B. 2) 6
C. 3) 4
D. 4) 8

Answer

To solve the problem, we need to find the banker's gain given the true discount and the amount due. Here’s a step-by-step solution:

### Step 1: Understand the given values
- The amount due (Debt) = Rs. 7440
- True Discount (TD) = Rs. 240
- Time = 16 months

### Step 2: Calculate the Present Worth (PW)
The Present Worth can be calculated using the formula:
\[ \text{Present Worth} = \text{Debt} - \text{True Discount} \]
Substituting the values:
\[ \text{PW} = 7440 - 240 = 7200 \]

### Step 3: Calculate the Banker's Gain (BG)
The formula for Banker's Gain is:
\[ \text{Banker's Gain} = \frac{\text{True Discount}^2}{\text{Present Worth}} \]
Substituting the values:
\[ \text{BG} = \frac{240^2}{7200} \]

### Step 4: Calculate \(240^2\)
Calculating \(240^2\):
\[ 240^2 = 57600 \]

### Step 5: Divide by Present Worth
Now, divide \(57600\) by \(7200\):
\[ \text{BG} = \frac{57600}{7200} = 8 \]

### Final Answer
The Banker's Gain is Rs. 8.

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