The present worth of a bill due sometime, hence is X 2200 and true discount on the bill is X 220. Find the banker's discount and banker's gain.

Options

A. BG = X 22 and BD = X 242
B. BG = X 242 and BD = X 22
C. BG = ? 11 and BD = ? 121
D. BG = X 31 and BD = X 343

Answer

To solve the problem, we need to find the Banker's Discount (BD) and the Banker's Gain (BG) using the given values for Present Worth (PW) and True Discount (TD).

### Step-by-Step Solution:

**Step 1: Identify the given values.**
- Present Worth (PW) = X 2200
- True Discount (TD) = X 220

**Step 2: Calculate the Banker's Discount (BD).**
The formula for Banker's Discount is:
\[ BD = PW + TD \]

Substituting the values:
\[ BD = 2200 + 220 \]
\[ BD = 2420 \]

**Step 3: Calculate the Banker's Gain (BG).**
The formula for Banker's Gain is:
\[ BG = \frac{TD^2}{PW} \]

Substituting the values:
\[ BG = \frac{220^2}{2200} \]
\[ BG = \frac{48400}{2200} \]
\[ BG = 22 \]

**Step 4: Final results.**
- Banker's Discount (BD) = X 2420
- Banker's Gain (BG) = X 22

### Summary of Results:
- Banker's Discount = X 2420
- Banker's Gain = X 22