A banker's paid 5767.20 for a bill of Rs. 5840, drawn on April 4 at 6 months. On what day was the bill discounted the rate of interest being `7%` ?

Options

A. 3rd Aug .
B. 4th Aug.
C. 3rd Sep.
D. 3rd July.

Answer

To solve the problem step by step, we will follow the process of calculating the banker's discount, the time period, and then determine the date the bill was discounted.

### Step 1: Calculate the Banker's Discount
The banker's discount can be calculated using the formula:
\[ \text{Banker's Discount} = \text{Face Value} - \text{Amount Paid} \]
Here, the face value of the bill is Rs 5840, and the amount paid is Rs 5767.20.

\[ \text{Banker's Discount} = 5840 - 5767.20 = 72.80 \]

### Step 2: Determine the Principal and Rate of Interest
The principal amount (face value of the bill) is Rs 5840, and the rate of interest is 7%.

### Step 3: Calculate the Time Period for the Banker's Discount
The formula for the banker's discount is given by:
\[ \text{Banker's Discount} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100} \]
We can rearrange this formula to find the time:
\[ \text{Time} = \frac{\text{Banker's Discount} \times 100}{\text{Principal} \times \text{Rate}} \]
Substituting the values:
\[ \text{Time} = \frac{72.80 \times 100}{5840 \times 7} \]
Calculating the denominator:
\[ 5840 \times 7 = 40880 \]
Now substituting back into the time formula:
\[ \text{Time} = \frac{7280}{40880} \approx 0.178 \text{ years} \]

### Step 4: Convert Time from Years to Months
To convert years into months, we multiply by 12:
\[ \text{Time in months} = 0.178 \times 12 \approx 2.13 \text{ months} \]
This is approximately 2 months and 4 days.

### Step 5: Determine the Date of Discounting
The bill was drawn on April 4 for 6 months. Therefore, the maturity date of the bill is:
\[ \text{Maturity Date} = \text{April 4} + 6 \text{ months} = \text{October 4} \]
Now, we subtract the unexpired time (approximately 2 months and 4 days) from the maturity date to find the date the bill was discounted:
\[ \text{Discount Date} = \text{October 4} - 2 \text{ months} - 4 \text{ days} = \text{August 30} \]

### Final Answer
The bill was discounted on **August 30**.

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