Simple interest on Rs 1200 at the rate of 13 pcpa for 'X' years is Rs 624. What is the interest on Rs 1200x at the same rate of interest for 3 years?

Options

A. Rs 1872
B. Rs 1384
C. Rs 939
D. None

Answer

To solve the problem step by step, we will use the formula for simple interest and follow the calculations as outlined in the video transcript.

### Step 1: Understand the Simple Interest Formula
The formula for calculating simple interest (SI) is:

\[ SI = \frac{P \times R \times T}{100} \]

where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 2: Set Up the Equation for the Given Information
We are given:
- Principal \( P = 1200 \)
- Rate \( R = 13\% \)
- Simple Interest \( SI = 624 \)
- Time \( T = X \) years

Using the formula, we can set up the equation:

\[ 624 = \frac{1200 \times 13 \times X}{100} \]

### Step 3: Simplify the Equation
To simplify the equation, we can multiply both sides by 100 to eliminate the fraction:

\[ 62400 = 1200 \times 13 \times X \]

Now, calculate \( 1200 \times 13 \):

\[ 1200 \times 13 = 15600 \]

So the equation becomes:

\[ 62400 = 15600 \times X \]

### Step 4: Solve for \( X \)
Now, divide both sides by 15600 to find \( X \):

\[ X = \frac{62400}{15600} \]

Calculating this gives:

\[ X = 4 \]

### Step 5: Calculate the New Principal
Now that we know \( X = 4 \), we need to find the interest on \( 1200X \) for 3 years. First, calculate the new principal:

\[ P = 1200 \times 4 = 4800 \]

### Step 6: Calculate the Interest for the New Principal
Now we will calculate the simple interest on \( 4800 \) at the same rate (13%) for 3 years:

Using the formula again:

\[ SI = \frac{P \times R \times T}{100} \]

Substituting the values:

\[ SI = \frac{4800 \times 13 \times 3}{100} \]

### Step 7: Simplify the Calculation
First, calculate \( 4800 \times 13 \):

\[ 4800 \times 13 = 62400 \]

Now substitute this back into the equation:

\[ SI = \frac{62400 \times 3}{100} \]

Calculating \( 62400 \times 3 \):

\[ 62400 \times 3 = 187200 \]

Now divide by 100:

\[ SI = \frac{187200}{100} = 1872 \]

### Final Answer
The interest on Rs 1200X at the same rate of interest for 3 years is Rs 1872.