The simple interest at y % for 'y' years will be Rs. y on a sum. Find the principal amount.
A.`100divy`
B. `100xx y`
C. `100y^(2)`
D. `100div y^(2)`

Options

A. C
B. D
C. A
D. B

Answer

To find the principal amount based on the given conditions, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We know that the simple interest (SI) at a rate of \( y\% \) for \( y \) years is equal to \( y \) rupees. We need to find the principal amount (P).

2. **Recall the Simple Interest Formula**: The formula for simple interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest (in percentage)
- \( T \) = Time (in years)

3. **Substitute the Given Values**: In our case:
- \( \text{SI} = y \)
- \( R = y \)
- \( T = y \)

Plugging these values into the formula gives:
\[ y = \frac{P \times y \times y}{100} \]

4. **Simplify the Equation**: We can simplify the equation:
\[ y = \frac{P \times y^2}{100} \]

5. **Eliminate \( y \) from Both Sides**: Since \( y \) is not zero, we can divide both sides by \( y \):
\[ 1 = \frac{P \times y}{100} \]

6. **Solve for Principal (P)**: Rearranging the equation to find \( P \):
\[ P = \frac{100}{y} \]

7. **Conclusion**: The principal amount \( P \) is \( \frac{100}{y} \).

### Final Answer:
The principal amount is \( \frac{100}{y} \).