Question

Loan at 12% SI for 3 years gives Rs. 5400 interest. Find principal.

• A. Rs.2000
• B. Rs.10000
• C. Rs.15000
• D. Rs.20000

Hint:

Remember the simple interest formula and be able to rearrange it to find any variable. Always double-check that the rate and time units are consistent (e.g., rate per annum, time in years).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The problem asks to calculate the principal amount of a loan, given the simple interest earned, the interest rate, and the duration of the loan.

Step 2: Key Formula or Approach:
The formula for Simple Interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) is the Principal amount.
- \( R \) is the Rate of interest per annum (in %).
- \( T \) is the Time period (in years).

Step 3: Detailed Explanation:
Given:
- Simple Interest (SI) = Rs. 5400.
- Rate of interest (R) = 12% per annum.
- Time period (T) = 3 years.
We need to find the Principal (P). Rearrange the SI formula:
\[ P = \frac{\text{SI} \times 100}{R \times T} \]
Substitute the given values:
\[ P = \frac{5400 \times 100}{12 \times 3} \]
\[ P = \frac{5400 \times 100}{36} \]
First, simplify $\frac{5400}{36}$:
$5400 \div 36 = 150$.
\[ P = 150 \times 100 \]
\[ P = \text{Rs. } 15,000 \]

Step 4: Final Answer:
The principal amount is Rs. 15,000.