In which time will the SI on Rs 4000 at 7.5% be Rs 1050 ?

Options

A. `2 (1)/(2)`yr
B. `5 (1)/(2)` yr
C. `3 (1)/(2)`yr
D. None of these

Answer

To solve the problem of finding the time required for the simple interest (SI) on Rs. 4000 at a rate of 7.5% to amount to Rs. 1050, we can use the formula for simple interest:

### Step-by-Step Solution:

1. **Identify the given values:**
- Principal (P) = Rs. 4000
- Rate (R) = 7.5%
- Simple Interest (SI) = Rs. 1050
- Time (T) = ?

2. **Use the formula for Simple Interest:**
\[ SI = \frac{P \times R \times T}{100} \]

3. **Substitute the known values into the formula:**
\[ 1050 = \frac{4000 \times 7.5 \times T}{100} \]

4. **Simplify the equation:**
- First, calculate \(4000 \times 7.5\):
\[ 4000 \times 7.5 = 30000 \]
- Substitute this back into the equation:
\[ 1050 = \frac{30000 \times T}{100} \]

5. **Further simplify:**
\[ 1050 = 300 \times T \]

6. **Isolate T by dividing both sides by 300:**
\[ T = \frac{1050}{300} \]

7. **Calculate T:**
\[ T = 3.5 \]

8. **Convert T into a fraction:**
- \(3.5\) can be expressed as \(\frac{7}{2}\) or \(2 \frac{1}{2}\) years.
- Alternatively, \(3.5\) can also be expressed as \(\frac{14}{4}\) which simplifies to \(\frac{7}{2}\).

### Final Answer:
The time required is \( \frac{7}{2} \) years or \( 3.5 \) years.

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