Priya invested a certain amount of money and got back an amount of Rs. 8800 after 3 years. If the rate of simple interest is 40 %, what is the principal amount invested by Priya?

Options

A. Rs. 7333
B. Rs. 4333
C. Rs. 4000
D. Rs. 7000

Answer

To find the principal amount invested by Priya, we can use the formula for simple interest and the information provided in the question.

### Step-by-step Solution:

1. **Identify the Given Information:**
- Amount received after 3 years (A) = Rs. 8800
- Rate of interest (R) = 40%
- Time period (T) = 3 years

2. **Use the Formula for Simple Interest:**
The formula for simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
where P is the principal amount.

3. **Relate Simple Interest to Amount:**
The amount (A) can also be expressed in terms of the principal and simple interest:
\[ A = P + SI \]
Therefore, we can rewrite the equation as:
\[ SI = A - P \]

4. **Substitute SI in the Formula:**
Substitute the expression for SI into the simple interest formula:
\[ A - P = \frac{P \times R \times T}{100} \]

5. **Plug in the Known Values:**
Substitute A = 8800, R = 40, and T = 3 into the equation:
\[ 8800 - P = \frac{P \times 40 \times 3}{100} \]

6. **Simplify the Equation:**
First, calculate the right side:
\[ 8800 - P = \frac{120P}{100} \]
This simplifies to:
\[ 8800 - P = 1.2P \]

7. **Combine Like Terms:**
Rearranging gives:
\[ 8800 = P + 1.2P \]
\[ 8800 = 2.2P \]

8. **Solve for P:**
Now, divide both sides by 2.2 to find P:
\[ P = \frac{8800}{2.2} \]
\[ P = 4000 \]

### Final Answer:
The principal amount invested by Priya is Rs. 4000.