A sum of Rs 12500 gives interest of Rs 5625 in T years at simple interest. If the rate of interest is 7.5%, then what will be the value of T?

Options

A. 5 years
B. 6 years
C. 7 years
D. 8 years

Answer

To find the value of T (time in years) for the given problem, we will use the formula for Simple Interest (SI):

### Step-by-Step Solution:

1. **Identify the given values**:
- Principal (P) = Rs 12,500
- Simple Interest (SI) = Rs 5,625
- Rate of Interest (R) = 7.5%

2. **Use the Simple Interest formula**:
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- R = Rate of Interest
- T = Time in years

3. **Substitute the known values into the formula**:
\[ 5625 = \frac{12500 \times 7.5 \times T}{100} \]

4. **Simplify the equation**:
- First, multiply both sides by 100 to eliminate the fraction:
\[ 562500 = 12500 \times 7.5 \times T \]

5. **Calculate \(12500 \times 7.5\)**:
\[ 12500 \times 7.5 = 93750 \]
So, the equation becomes:
\[ 562500 = 93750 \times T \]

6. **Solve for T**:
- Divide both sides by 93750:
\[ T = \frac{562500}{93750} \]

7. **Calculate the value of T**:
\[ T = 6 \]

### Final Answer:
The value of T is **6 years**.