A bill was drawn on 14th April for Rs.7,000 and was discounted on 6th July at 5% p.a. The Banker paid Rs.6,930 for the bill. What is the legal due date.

Answer

To find the legal due date of the bill that was drawn on April 14 for Rs. 7,000 and discounted on July 6 at a rate of 5% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Face Value (FV) of the bill = Rs. 7,000
- Cash Value (CV) received after discounting = Rs. 6,930
- Discount Date = July 6
- Rate of Interest (r) = 5% per annum

2. **Calculate the Banker's Discount (BD):**
\[ \text{Banker's Discount (BD)} = \text{Face Value} - \text{Cash Value} \]
\[ BD = 7000 - 6930 = 70 \text{ Rs.} \]

3. **Set Up the Formula for Banker's Discount:**
The formula for Banker's Discount is given by:
\[ BD = \frac{FV \times n \times r}{100 \times 365} \]
Where:
- \( n \) = number of days before the legal due date when the bill was discounted
- \( r \) = rate of interest (5%)

4. **Substitute the Known Values into the Formula:**
\[ 70 = \frac{7000 \times n \times 5}{100 \times 365} \]

5. **Simplify the Equation:**
\[ 70 = \frac{7000 \times n \times 5}{36500} \]
\[ 70 \times 36500 = 7000 \times n \times 5 \]
\[ 2555000 = 35000n \]
\[ n = \frac{2555000}{35000} = 73 \]

6. **Determine the Legal Due Date:**
Since the bill was discounted 73 days before the legal due date, we need to add 73 days to the discount date (July 6).
- July has 31 days, so from July 6 to July 31 is 25 days.
- This leaves us with \( 73 - 25 = 48 \) days to account for in August and September.
- August has 31 days, so from August 1 to August 31 is 31 days.
- This leaves us with \( 48 - 31 = 17 \) days to account for in September.

7. **Calculate the Final Legal Due Date:**
- Adding 17 days to September 1 gives us September 17.

### Final Answer:
The legal due date of the bill is **September 17**.