Find the difference between the banker's discount and the true discount on Rs. 8100 for 3 months at `5%`-----

Options

A. Rs.0.125
B. Rs.1.25
C. Rs.12.5
D. None of these

Answer

To find the difference between the banker's discount (BD) and the true discount (TD) on Rs. 8100 for 3 months at a rate of 5%, we can follow these steps:

### Step 1: Calculate the Banker's Discount (BD)
The formula for the Banker's Discount is given by:

\[ BD = \frac{P \times R \times T}{100} \]

Where:
- \( P \) = Principal amount (Rs. 8100)
- \( R \) = Rate of interest (5%)
- \( T \) = Time in years (3 months = \(\frac{3}{12} = \frac{1}{4}\) years)

Substituting the values:

\[ BD = \frac{8100 \times 5 \times \frac{1}{4}}{100} \]

Calculating this gives:

\[ BD = \frac{8100 \times 5 \times 0.25}{100} = \frac{10125}{100} = 101.25 \]

### Step 2: Calculate the True Discount (TD)
The formula for the True Discount is given by:

\[ TD = \frac{P \times R \times T}{100 + R \times T} \]

Using the same values:

\[ TD = \frac{8100 \times 5 \times \frac{1}{4}}{100 + 5 \times \frac{1}{4}} \]

Calculating the denominator:

\[ 100 + 5 \times \frac{1}{4} = 100 + 1.25 = 101.25 \]

Now substituting back into the TD formula:

\[ TD = \frac{8100 \times 5 \times 0.25}{101.25} \]

Calculating the numerator:

\[ 8100 \times 5 \times 0.25 = 10125 \]

Now, substituting into the TD formula:

\[ TD = \frac{10125}{101.25} = 100 \]

### Step 3: Find the Difference between BD and TD
Now we can find the difference:

\[ \text{Difference} = BD - TD = 101.25 - 100 = 1.25 \]

### Final Answer
The difference between the banker's discount and the true discount is Rs. 1.25.

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