For what sum will the simple interest at R % per annum for 2 years will be R ?

Options

A. Rs. `(100)/(2R)`
B. Rs.50
C. Rs.`(100)/(R )`
D. Rs. `(200)/(R )`

Answer

To solve the problem, we need to find the principal sum (P) for which the simple interest (SI) at a rate of R% per annum for 2 years will equal R.

### Step-by-Step Solution:

1. **Understand the Simple Interest Formula**:
The formula for simple interest is given by:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount (the sum we want to find)
- \( R \) = Rate of interest (in percentage)
- \( T \) = Time (in years)

2. **Substitute the Given Values**:
According to the problem:
- Simple Interest \( SI = R \)
- Rate \( R = R\% \)
- Time \( T = 2 \) years

Substitute these values into the formula:
\[ R = \frac{P \times R \times 2}{100} \]

3. **Rearrange the Equation**:
To isolate \( P \), we can rearrange the equation:
\[ R = \frac{2PR}{100} \]
Multiply both sides by 100 to eliminate the fraction:
\[ 100R = 2PR \]

4. **Divide Both Sides by R**:
Assuming \( R \neq 0 \), we can divide both sides by \( R \):
\[ 100 = 2P \]

5. **Solve for P**:
Now, divide both sides by 2:
\[ P = \frac{100}{2} = 50 \]

Thus, the principal sum \( P \) for which the simple interest at R% per annum for 2 years will equal R is **50**.

### Final Answer:
The required sum is **50**.