The true discount on a bill of Rs. 1860 due after 8 months is Rs. 60. Find the banker's discount -----

Options

A. Rs.62
B. Rs.52
C. Rs. 60
D. None of these

Answer

To find the banker's discount on a bill of Rs. 1860 due after 8 months with a true discount of Rs. 60, we can follow these steps:

### Step 1: Identify the given values
- Amount (A) = Rs. 1860
- True Discount (TD) = Rs. 60
- Time (T) = 8 months

### Step 2: Calculate the Present Worth (PW)
The present worth can be calculated using the formula:
\[ \text{Present Worth (PW)} = \text{Amount} - \text{True Discount} \]
Substituting the values:
\[ \text{PW} = 1860 - 60 = 1800 \]

### Step 3: Calculate the Rate of Interest (R)
The true discount formula is:
\[ \text{True Discount} = \frac{\text{Present Worth} \times \text{Rate} \times \text{Time}}{100} \]
Rearranging the formula to find the rate:
\[ \text{Rate} = \frac{\text{True Discount} \times 100}{\text{Present Worth} \times \text{Time}} \]
Substituting the values:
- Time in years = \( \frac{8}{12} = \frac{2}{3} \) years
\[ \text{Rate} = \frac{60 \times 100}{1800 \times \frac{2}{3}} \]
Calculating:
\[ \text{Rate} = \frac{6000}{1200} = 5\% \]

### Step 4: Calculate the Banker's Discount (BD)
The banker's discount is calculated using the formula:
\[ \text{Banker's Discount} = \frac{\text{Amount} \times \text{Rate} \times \text{Time}}{100} \]
Substituting the values:
\[ \text{BD} = \frac{1860 \times 5 \times \frac{2}{3}}{100} \]
Calculating:
\[ \text{BD} = \frac{1860 \times 5 \times 0.6667}{100} \]
\[ \text{BD} = \frac{6200}{100} = 62 \]

### Final Answer
The banker's discount is Rs. 62.

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