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.

Answer 2

Since the simple interest formula is straightforward to apply forward, each candidate principal can be tested directly by computing the interest it would generate at 12% for 3 years and comparing that to the given interest of Rs. 5400.

1. Rs. 2000: Interest \( = \frac{2000 \times 12 \times 3}{100} = \frac{72000}{100} = 720 \), far short of the required Rs. 5400.
2. Rs. 10000: Interest \( = \frac{10000 \times 12 \times 3}{100} = \frac{360000}{100} = 3600 \), still less than Rs. 5400.
3. Rs. 15000: Interest \( = \frac{15000 \times 12 \times 3}{100} = \frac{540000}{100} = 5400 \), matching the given interest exactly.
4. Rs. 20000: Interest \( = \frac{20000 \times 12 \times 3}{100} = \frac{720000}{100} = 7200 \), which overshoots the required Rs. 5400.

Testing each option forward through the simple interest formula shows that only a principal of Rs. 15000 produces exactly Rs. 5400 in interest over 3 years at 12%.

Therefore, the correct answer is Rs. 15000.