The true discount on a bill of Rs 900 is Rs 100. Find the banker's discount.

Answer

To solve the problem of finding the banker's discount when the true discount on a bill of Rs 900 is Rs 100, we can follow these steps:

### Step 1: Understand the Definitions
- **True Discount (TD)**: The difference between the nominal value (or face value) of the bill and its present worth (PW).
- **Banker's Discount (BD)**: The discount calculated on the face value of the bill.

### Step 2: Identify Given Values
- True Discount (TD) = Rs 100
- Present Worth (PW) = Rs 900

### Step 3: Use the Formula for True Discount
The formula for True Discount is:
\[ \text{TD} = \sqrt{\text{PW} \times \text{Banker's Gain (BG)}} \]

### Step 4: Rearrange the Formula
We can rearrange the formula to find the Banker's Gain (BG):
\[ \text{BG} = \frac{\text{TD}^2}{\text{PW}} \]

### Step 5: Substitute the Known Values
Substituting the known values into the rearranged formula:
\[ \text{BG} = \frac{100^2}{900} \]
\[ \text{BG} = \frac{10000}{900} \]
\[ \text{BG} = \frac{1000}{90} \]
\[ \text{BG} = \frac{100}{9} \]
\[ \text{BG} \approx 11.11 \]

### Step 6: Calculate Banker's Discount
The Banker's Discount (BD) is calculated as:
\[ \text{BD} = \text{Banker's Gain (BG)} + \text{True Discount (TD)} \]
Substituting the values we have:
\[ \text{BD} = \frac{100}{9} + 100 \]
\[ \text{BD} = 11.11 + 100 \]
\[ \text{BD} \approx 111.11 \]

### Final Answer
The Banker's Discount is approximately Rs 111.11.

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