Question

A certain sum of money is borrowed by a person at 8% simple interest for 4 years. If he has to pay Rs. 7834 as interest, what is the total amount he has to pay?

• A. Rs. 23073
• B. Rs. 30459
• C. Rs. 37853
• D. Rs. 14768

Hint:

Simple Interest is directly proportional to the Principal. The total interest is \( 8% \times 4 = 32% \) of the Principal. Therefore, the Principal is \( \frac{100}{32} \) of the interest, and the Total Amount is \( \frac{132}{32} \) of the interest.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We need to calculate the total amount (Principal + Interest) paid at the end of a 4-year period given the simple interest rate and the total interest paid.
Note: Based on the provided options, there is a typographical error in the question text. The interest amount should logically be Rs. 7384 (a common transposition error from 7834) to match the given choices. The solution below assumes this intended value.


Step 2: Key Formula or Approach:
Simple Interest (\( \text{SI} \)) formula: \( \text{SI} = \frac{P \times R \times T}{100} \)
Total Amount (\( A \)) formula: \( A = P + \text{SI} \)
Where \( P \) is Principal, \( R \) is Rate, and \( T \) is Time.


Step 3: Detailed Explanation:
Given values (assuming corrected interest):
\( \text{SI} = \text{Rs. } 7384 \)
\( R = 8% \)
\( T = 4 \text{ years} \)
First, find the Principal (\( P \)):
\[ 7384 = \frac{P \times 8 \times 4}{100} \] \[ 7384 = \frac{32P}{100} \] \[ P = \frac{7384 \times 100}{32} \] \[ P = 230.75 \times 100 = 23075 \] So, the Principal borrowed is Rs. 23,075.
Now, calculate the total amount to be paid back:
\[ \text{Total Amount} = \text{Principal} + \text{Simple Interest} \] \[ \text{Total Amount} = 23075 + 7384 = 30459 \] This matches option (B).
*(If we strictly used 7834, the Principal would be \( 24481.25 \) and the Amount would be \( 32315.25 \), which is not among the options.)*


Step 4: Final Answer:
The total amount he has to pay is Rs. 30459.