Tushar borrowed Rs 12,000 from a money lender at rate 15% per annum as 13th January 1987 and he returned his loan on 8 June 1987. What was the amount given by Tushar to money lender for payment of loan?

Options

A. Rs 15,000
B. Rs 11,394
C. Rs 12,720
D. Rs 13,650

Answer

To solve the problem, we will calculate the Simple Interest (SI) that Tushar has to pay on the borrowed amount. Here’s the step-by-step solution:

### Step 1: Identify the given values
- Principal (P) = Rs 12,000
- Rate (R) = 15% per annum
- Time (T) = From 13th January 1987 to 8th June 1987

### Step 2: Calculate the time in days
To calculate the time in days, we need to count the number of days from 13th January to 8th June.

- January: 18 days (from 13th to 31st)
- February: 28 days (1987 is not a leap year)
- March: 31 days
- April: 30 days
- May: 31 days
- June: 8 days

Now, add these days together:
\[ \text{Total Days} = 18 + 28 + 31 + 30 + 31 + 8 = 146 \text{ days} \]

### Step 3: Convert days into years
To convert days into years, we divide the total days by 365 (since there are 365 days in a year):
\[ T = \frac{146}{365} \text{ years} \]

### Step 4: Calculate Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]

Substituting the values we have:
\[ SI = \frac{12000 \times 15 \times \frac{146}{365}}{100} \]

### Step 5: Simplify the calculation
First, calculate \( \frac{12000 \times 15}{100} \):
\[ \frac{12000 \times 15}{100} = 1800 \]

Now, calculate the interest:
\[ SI = 1800 \times \frac{146}{365} \]

Next, calculate \( 1800 \times \frac{146}{365} \):
\[ SI = 1800 \times 0.4000 \approx 720 \]

### Step 6: Calculate the total amount paid
The total amount paid (A) is the sum of the principal and the interest:
\[ A = P + SI \]
\[ A = 12000 + 720 = 12720 \]

### Final Answer
The total amount given by Tushar to the money lender for payment of the loan is **Rs 12,720**.

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