In how many years will a man get a simple interest on Rs.1,428/- on a principal of Rs. 4,080/at the rate of 7 p c p.a.?

Options

A. 4years
B. 6years
C. 5 years
D. 8years

Answer

To solve the problem of finding out how many years it will take for a man to earn a simple interest of Rs. 1,428 on a principal of Rs. 4,080 at a rate of 7% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Principal (P) = Rs. 4,080
- Simple Interest (SI) = Rs. 1,428
- Rate of interest (R) = 7% per annum

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

3. **Substitute the known values into the formula:**
\[ 1428 = \frac{4080 \times 7 \times T}{100} \]

4. **Simplify the equation:**
- Multiply both sides by 100 to eliminate the fraction:
\[ 142800 = 4080 \times 7 \times T \]

5. **Calculate \(4080 \times 7\):**
\[ 4080 \times 7 = 28560 \]
So the equation now is:
\[ 142800 = 28560 \times T \]

6. **Solve for T:**
- Divide both sides by 28560:
\[ T = \frac{142800}{28560} \]

7. **Perform the division:**
- Simplifying \( \frac{142800}{28560} \):
\[ T = 5 \]

8. **Conclusion:**
- Therefore, the time (T) required to earn a simple interest of Rs. 1,428 is **5 years**.

### Final Answer:
The man will get a simple interest of Rs. 1,428 in **5 years**.

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