The true discount at a bill of ? 3720 due 8 months hence is X 120. Find the banker's gain.

Answer

To solve the problem of finding the banker's gain given the true discount and the bill amount, we can follow these steps:

### Step 1: Understand the Given Information
We are given:
- The amount of the bill (due amount) = ₹3720
- The true discount (TD) = ₹120
- The time until the bill is due = 8 months

### Step 2: Calculate the Present Worth (PW)
The present worth can be calculated using the formula:
\[ \text{Present Worth (PW)} = \text{Due Amount} - \text{True Discount} \]
Substituting the values:
\[ \text{PW} = 3720 - 120 = 3600 \]

### Step 3: Use the Banker's Gain Formula
The formula for banker's gain (BG) is:
\[ \text{Banker's Gain (BG)} = \frac{(\text{True Discount})^2}{\text{Present Worth}} \]
Substituting the values we have:
\[ \text{BG} = \frac{120^2}{3600} \]

### Step 4: Calculate the Banker's Gain
Now, calculate \(120^2\):
\[ 120^2 = 14400 \]
Now substitute this back into the formula:
\[ \text{BG} = \frac{14400}{3600} \]

### Step 5: Simplify the Calculation
Now simplify:
\[ \text{BG} = 4 \]

### Final Answer
Thus, the banker's gain is ₹4.

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