A bill for Rs. 5656 is drawn on july 14 at 5 months. It is discounted on Oct. 5th at `5%`-----
Money received by the holder of the bill -----

Options

A. Rs.5599.56
B. Rs.5599.44
C. Rs.5599
D. None of these

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the Amount and Time
The amount of the bill is Rs. 5656, and it is drawn for 5 months starting from July 14.

**Hint:** Remember to note the amount and the duration for which the bill is drawn.

### Step 2: Determine the Due Date
The bill is drawn on July 14 for 5 months. Therefore, the nominal due date will be:
- July 14 + 5 months = December 14.

**Hint:** When calculating the due date, add the number of months to the initial date.

### Step 3: Calculate the Time Remaining Until the Due Date
The bill is discounted on October 5. We need to calculate the time remaining from October 5 to December 14.

1. From October 5 to October 31 = 26 days
2. All of November = 30 days
3. From December 1 to December 14 = 14 days

Total days remaining = 26 + 30 + 14 = 70 days.

**Hint:** Break down the calculation into segments (full months and remaining days) to make it easier.

### Step 4: Convert Days to Years
To calculate the time in years, we convert the total days into years:
- Time in years = 70 days / 365 days = 70/365 = 14/73 years (approximately).

**Hint:** Remember that there are 365 days in a year when converting days to years.

### Step 5: Calculate the Banker's Discount
The Banker's Discount (BD) can be calculated using the formula:
\[ \text{BD} = \text{Amount} \times \text{Rate} \times \text{Time} / 100 \]

Substituting the values:
- Amount = 5656
- Rate = 5%
- Time = 70/365

\[ \text{BD} = 5656 \times 5 \times \frac{70}{365} / 100 \]

Calculating this:
\[ \text{BD} = 5656 \times 5 \times \frac{70}{36500} \]
\[ \text{BD} = 5656 \times 0.0095890411 \]
\[ \text{BD} \approx 54.24 \]

**Hint:** Make sure to multiply the amount by the rate and time correctly, and remember to divide by 100.

### Step 6: Calculate Money Received by the Holder
The money received by the holder of the bill is calculated by subtracting the Banker's Discount from the amount of the bill:
\[ \text{Money Received} = \text{Amount} - \text{BD} \]
\[ \text{Money Received} = 5656 - 54.24 \]
\[ \text{Money Received} \approx 5601.76 \]

**Hint:** Always subtract the Banker's Discount from the original amount to find out how much money is received.

### Final Answer
The money received by the holder of the bill is approximately Rs. 5601.76.