Veer invested an amount on simple interest, and it becomes two times of itself in 10 years. If Veer invested Rs. X at the same rate of interest on Cl and he gets Rs. 5324 as amount after three years, then find amount invested by Veer (in Rs.)?

Options

A. 4400
B. 3600
C. 4800
D. 4000

Answer

To solve the problem step by step, we will break down the information given and apply the relevant formulas for simple interest and compound interest.

### Step 1: Understanding the Simple Interest Scenario
Veer invested an amount that doubled in 10 years. Let's denote the principal amount as \( P \).

Given:
- Amount after 10 years = \( 2P \)
- Time = 10 years

The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( SI \) = Simple Interest
- \( P \) = Principal
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

Since the amount doubled, the interest earned in 10 years is equal to the principal:
\[ SI = 2P - P = P \]

### Step 2: Setting Up the Equation
Using the SI formula:
\[ P = \frac{P \times R \times 10}{100} \]

### Step 3: Simplifying the Equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 1 = \frac{R \times 10}{100} \]
\[ R = 10\% \]

### Step 4: Understanding the Compound Interest Scenario
Now, Veer invests an amount \( X \) at the same rate of interest (10%) but on compound interest (CI) for 3 years, and the total amount received is Rs. 5324.

The formula for Compound Interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \( A \) = Amount after time \( T \)
- \( P \) = Principal
- \( R \) = Rate of interest
- \( T \) = Time in years

Given:
- \( A = 5324 \)
- \( R = 10\% \)
- \( T = 3 \)

### Step 5: Setting Up the CI Equation
Substituting the known values into the CI formula:
\[ 5324 = X \left(1 + \frac{10}{100}\right)^3 \]
\[ 5324 = X \left(1.1\right)^3 \]

### Step 6: Calculating \( (1.1)^3 \)
Calculating \( (1.1)^3 \):
\[ (1.1)^3 = 1.1 \times 1.1 \times 1.1 = 1.331 \]

### Step 7: Substituting Back to Find \( X \)
Now substituting back:
\[ 5324 = X \times 1.331 \]
To find \( X \):
\[ X = \frac{5324}{1.331} \]

### Step 8: Performing the Division
Calculating \( X \):
\[ X \approx 4000 \]

### Conclusion
Thus, the amount invested by Veer is Rs. 4000.