At what rate of simple interest per annum, does the interest on Rs. 1200 in 2 years equals the interest on Rs. 600 at 4 years at `(7)/(2)%` per annum ?

Options

A. `(3)/(4)%`
B. `(7)/(2)%`
C. `(4)/(3)%`
D. `(7)/(8)%`

Explanation

To solve the problem, we need to find the rate of simple interest per annum (R) such that the interest on Rs. 1200 in 2 years equals the interest on Rs. 600 at 4 years at a rate of \( \frac{7}{2}\% \) per annum.

### Step-by-Step Solution:

1. **Understand the Simple Interest Formula**:
The formula for calculating Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
where \( P \) is the principal amount, \( R \) is the rate of interest per annum, and \( T \) is the time in years.

2. **Calculate the Interest for Rs. 600 at \( \frac{7}{2}\% \) for 4 years**:
- Here, \( P = 600 \), \( R = \frac{7}{2} \), and \( T = 4 \).
- Substitute these values into the SI formula:
\[ SI_2 = \frac{600 \times \frac{7}{2} \times 4}{100} \]

3. **Calculate \( SI_2 \)**:
- First, calculate \( \frac{7}{2} \times 4 = 14 \).
- Then, substitute back into the formula:
\[ SI_2 = \frac{600 \times 14}{100} = \frac{8400}{100} = 84 \]

4. **Set Up the Equation for Rs. 1200 in 2 years**:
- Let \( R \) be the unknown rate of interest.
- Here, \( P = 1200 \), \( T = 2 \).
- The equation for the interest on Rs. 1200 becomes:
\[ SI_1 = \frac{1200 \times R \times 2}{100} \]

5. **Set \( SI_1 \) Equal to \( SI_2 \)**:
- Since we want \( SI_1 = SI_2 \):
\[ \frac{1200 \times R \times 2}{100} = 84 \]

6. **Solve for \( R \)**:
- Simplify the left side:
\[ \frac{2400R}{100} = 84 \]
- This simplifies to:
\[ 24R = 84 \]
- Now, divide both sides by 24:
\[ R = \frac{84}{24} = 3.5 \]

7. **Convert to Percentage**:
- Since \( R \) is already in percentage, we can state:
\[ R = 3.5\% \]

### Final Answer:
The rate of simple interest per annum is \( 3.5\% \).