Question

A sum of rupees fetches simple interest Rs.2400 for 2 years. If the rate of interest is 12%, then the principal amount is

• A. Rs.12000
• B. Rs.10000.
• C. Rs.8000
• D. Rs.10200

Hint:

A simple interest rate of 12% per year for 2 years means total interest accumulated is:
\[ 12\% \times 2 = 24\% \text{ of the principal} \]
If 24% of the principal is Rs.2400, then 1% is Rs.100.
Therefore, 100% (the entire Principal) must be $100 \times 100 = \text{Rs.}10000$.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question involves the calculation of Simple Interest ($SI$).
We are given:
- Simple Interest ($SI$) = Rs.2400
- Time period ($T$) = 2 years
- Rate of interest ($R$) = 12% per annum
We need to find the Principal amount ($P$).

Step 2: Key Formula or Approach:
The standard formula for calculating Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
To find the Principal ($P$), we can rearrange the formula:
\[ P = \frac{SI \times 100}{R \times T} \]

Step 3: Detailed Calculation:
Substitute the given values into the rearranged formula:
- $SI = 2400$
- $T = 2$
- $R = 12$
\[ P = \frac{2400 \times 100}{12 \times 2} \]
Simplify the denominator:
\[ 12 \times 2 = 24 \]
Substitute back:
\[ P = \frac{2400 \times 100}{24} \]
Notice that $2400 \div 24 = 100$:
\[ P = 100 \times 100 \]
\[ P = 10000 \]
Thus, the principal amount is Rs.10000.

Step 4: Final Answer:
This matches Option (B).