The simple interest at x% for x years will be Rs. x on a sum of:

Options

A. x
B. Rs `((100)/(x))`
C. Rs `((100)/(x^(2)))`
D. None of these

Answer

To solve the problem, we need to find the principal amount (P) on which the simple interest (SI) at a rate of x% for x years will amount to Rs. x.

### Step-by-step Solution:

1. **Understand the Simple Interest Formula**:
The formula for calculating Simple Interest is:
\[ SI = \frac{P \times r \times t}{100} \]
where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount
- \( r \) = Rate of interest (in percentage)
- \( t \) = Time (in years)

2. **Identify the Given Values**:
From the problem, we know:
- \( SI = x \) (the interest earned is Rs. x)
- \( r = x\% \) (the rate of interest is x percent)
- \( t = x \) (the time period is x years)

3. **Substitute the Values into the Formula**:
Plugging the known values into the Simple Interest formula:
\[ x = \frac{P \times x \times x}{100} \]

4. **Rearranging the Equation**:
To find \( P \), we can rearrange the equation:
\[ x = \frac{P \times x^2}{100} \]
Multiplying both sides by 100 to eliminate the fraction:
\[ 100x = P \times x^2 \]

5. **Solving for Principal (P)**:
Now, divide both sides by \( x^2 \) (assuming \( x \neq 0 \)):
\[ P = \frac{100x}{x^2} \]
Simplifying this gives:
\[ P = \frac{100}{x} \]

### Final Answer:
The principal amount (P) is:
\[ P = \frac{100}{x} \]