Question

A farmers borrowed Rs. 3000 at 12% simple interest per annum. At the end of 4 years he cleared this account by paying Rs. 3200 and a cow. The cost of the cow is Rs. :

• A. 1260
• B. 1240
• C. 4440
• D. 1640

Hint:

Always calculate the total due amount first. The value of any commodity given in lieu of cash to settle a debt is simply the difference between the total amount due and the cash paid.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Simple interest is calculated solely on the initial principal borrowed.
To clear a debt, the borrower must pay back the total accumulated amount, which is the sum of the principal and the simple interest.
Key Formula or Approach:
The Simple Interest (SI) formula is: \[ \text{SI} = \frac{P \cdot R \cdot T}{100} \] The total accumulated amount ($A$) is: \[ A = P + \text{SI} \] where:
- $P$ is the principal amount.
- $R$ is the annual interest rate.
- $T$ is the duration in years.

Step 2: Detailed Explanation:
Let's list the given parameters:
- Principal ($P$) = Rs. $3000$
- Interest Rate ($R$) = $12%$ per annum
- Time ($T$) = $4$ years
Let's compute the Simple Interest: \[ \text{SI} = \frac{3000 \cdot 12 \cdot 4}{100} \] \[ \text{SI} = 30 \cdot 48 = 1440 \] Thus, the total amount ($A$) to be repaid to clear the account is: \[ A = 3000 + 1440 = 4440 \text{ Rs.} \] The farmer pays Rs. $3200$ in cash and gives a cow to settle the debt.
Let the cost of the cow be $C$.
Therefore: \[ \text{Cash Paid} + \text{Cost of the Cow} = \text{Total Repayment Amount} \] \[ 3200 + C = 4440 \] Solve for $C$: \[ C = 4440 - 3200 = 1240 \text{ Rs.} \]

Step 3: Final Answer:
The cost of the cow is Rs. 1240.