Ram borrowed a sum of Rs. 12000 at 15% per annum from a money lender on 13th January, 2003 and returned the amount on 8th June, 2003 to clear his debt. What was the amount paid by Ram to the money-lender to clear his debt ?

Options

A. a) Rs.15000
B. b) Rs. 11394
C. c) Rs. 12720
D. d) Rs. 13650

Answer

To find the total amount Ram paid to the money lender, we need to calculate the simple interest for the period he borrowed the money and then add that interest to the principal amount.

### Step-by-Step Solution:

1. **Identify the Principal Amount (P)**:
- Ram borrowed Rs. 12,000.
- \( P = 12000 \)

2. **Identify the Rate of Interest (R)**:
- The rate of interest is 15% per annum.
- \( R = 15\% \)

3. **Calculate the Time Period (T)**:
- Ram borrowed the money on 13th January 2003 and returned it on 8th June 2003.
- We need to calculate the total number of days between these two dates.

- **Days in January**: From 13th to 31st January = \( 31 - 13 = 18 \) days
- **Days in February**: 28 days (2003 is not a leap year)
- **Days in March**: 31 days
- **Days in April**: 30 days
- **Days in May**: 31 days
- **Days in June**: From 1st to 8th June = 8 days

- **Total Days**:
\[ 18 + 28 + 31 + 30 + 31 + 8 = 146 \text{ days} \]

- Convert days into years:
\[ T = \frac{146}{365} \text{ years} \]

4. **Calculate Simple Interest (SI)**:
- The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
- Substituting the values:
\[ SI = \frac{12000 \times 15 \times \frac{146}{365}}{100} \]

- Calculate:
\[ SI = \frac{12000 \times 15 \times 146}{36500} \]
\[ SI = \frac{26160000}{36500} \approx 717.81 \text{ (approximately Rs. 720)} \]

5. **Calculate the Total Amount Paid (A)**:
- The total amount paid is the sum of the principal and the simple interest:
\[ A = P + SI \]
- Substituting the values:
\[ A = 12000 + 720 = 12720 \]

### Final Answer:
Ram paid a total of Rs. 12,720 to the money lender.

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