Question

Chirag takes some loan from Dinesh for 2 years at the rate of 10% per annum. And after 2 years, he gave back Rs 6000 to Dinesh and completed the payment of his loan. The interest paid by Chirag is:

• A. Rs 1002
• B. Rs 1200
• C. Rs 1000
• D. Rs 1020

Hint:

An alternate, quick way is to use percentages:
The simple interest for 2 years at 10% per annum is $2 \times 10\% = 20\%$ of the principal.
So, the total amount returned is $100\% + 20\% = 120\%$ of the principal.
If $120\% = 6000$, then the interest ($20\%$) is: \[ \text{Interest} = \frac{6000}{120} \times 20 = 50 \times 20 = 1000 \] This percentage approach is faster and less prone to calculation mistakes.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question involves simple interest on a loan.
Chirag borrows a principal sum ($P$) for a duration of 2 years at an interest rate of 10% per annum.
At the end of 2 years, he pays back the total accumulated amount ($A$) of Rs 6000 to settle the loan.
We need to determine the interest component of this final payment.

Step 2: Key Formula or Approach:
The relation between the Principal ($P$), Rate ($R$), Time ($T$), and Simple Interest ($SI$) is: \[ SI = \frac{P \times R \times T}{100} \] The total Amount ($A$) returned is: \[ A = P + SI = P + \frac{P \times R \times T}{100} = P \left(1 + \frac{R \times T}{100}\right) \] Once the Principal is calculated, the Interest can be found using: \[ SI = A - P \]

Step 3: Detailed Explanation:

• Identify the Given Values: Amount ($A$) paid = Rs 6000
Rate of interest ($R$) = 10% per annum
Time period ($T$) = 2 years

• Calculate the Principal ($P$): Using the amount formula: \[ 6000 = P \left(1 + \frac{10 \times 2}{100}\right) \] Simplify the expression inside the parenthesis: \[ 6000 = P \left(1 + \frac{20}{100}\right) = P (1 + 0.2) \] \[ 6000 = 1.2P \] Now, solve for $P$: \[ P = \frac{6000}{1.2} = \frac{60000}{12} = 5000 \] So, the principal amount borrowed was Rs 5000.

• Calculate the Interest Component ($SI$): \[ SI = A - P \] \[ SI = 6000 - 5000 = 1000 \] The interest paid by Chirag is Rs 1000.

Step 4: Final Answer:
The interest paid on the loan is Rs 1000.
Therefore, the correct option is (C).