What is the sum of amount which gives Rs. 6300 as interest @7% per annum of simple interest is 7 `1/2` years ?

Options

A. 36000
B. 24000
C. 63000
D. 12000

Answer

To find the principal amount that gives Rs. 6300 as interest at a rate of 7% per annum over a period of 7.5 years using simple interest, we can use the formula for simple interest:

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

Where:
- \( SI \) = Simple Interest
- \( P \) = Principal Amount
- \( R \) = Rate of Interest
- \( T \) = Time (in years)

### Step 1: Identify the given values
From the question, we have:
- \( SI = 6300 \) (the interest earned)
- \( R = 7\% \) (the rate of interest)
- \( T = 7.5 \) years (the time period)

### Step 2: Substitute the values into the formula
We can rearrange the formula to solve for \( P \):

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

Now substituting the values into the formula:

\[ P = \frac{6300 \times 100}{7 \times 7.5} \]

### Step 3: Calculate the denominator
Calculating \( R \times T \):

\[ R \times T = 7 \times 7.5 = 52.5 \]

### Step 4: Substitute back into the formula
Now substituting back into the equation for \( P \):

\[ P = \frac{6300 \times 100}{52.5} \]

### Step 5: Calculate the numerator
Calculating \( 6300 \times 100 \):

\[ 6300 \times 100 = 630000 \]

### Step 6: Final calculation
Now divide the numerator by the denominator:

\[ P = \frac{630000}{52.5} \]

Calculating this gives:

\[ P = 12000 \]

### Conclusion
The principal amount \( P \) is Rs. 12000.