Bhavya and Veer invested their principle in two different schemes, Bhavya invested X Rs.on compound interest for two year at rate of 20% annually and Veer invested 4000 Rs. more than Bhavya on simple interest for three year at 15% annually, if both gets total interest of Rs. 9632, then Find the amount invested by Veer?

Options

A. A)12900
B. B)12400
C. C)8800
D. D)12800

Answer

To solve the problem step by step, we will break down the investments of Bhavya and Veer, calculate the interests they earned, and then find the amount invested by Veer.

### Step 1: Define the variables
Let:
- \( X \) = amount invested by Bhavya (in Rs.)
- Therefore, the amount invested by Veer = \( X + 4000 \) (in Rs.)

### Step 2: Calculate the interest earned by Bhavya
Bhavya invested \( X \) Rs. at a compound interest rate of 20% per annum for 2 years. The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( A \) = total amount after interest
- \( P \) = principal amount (initial investment)
- \( r \) = rate of interest
- \( n \) = number of years

For Bhavya:
\[ A = X \left(1 + \frac{20}{100}\right)^2 = X \left(1.2\right)^2 = X \times 1.44 \]
The interest earned by Bhavya is:
\[ \text{Interest} = A - P = 1.44X - X = 0.44X \]

### Step 3: Calculate the interest earned by Veer
Veer invested \( X + 4000 \) Rs. at a simple interest rate of 15% per annum for 3 years. The formula for simple interest is:
\[ \text{SI} = \frac{P \times r \times t}{100} \]
For Veer:
\[ \text{SI} = \frac{(X + 4000) \times 15 \times 3}{100} = \frac{(X + 4000) \times 45}{100} = 0.45(X + 4000) \]
The interest earned by Veer is:
\[ \text{Interest} = 0.45(X + 4000) = 0.45X + 1800 \]

### Step 4: Set up the equation based on total interest
According to the problem, the total interest earned by both Bhavya and Veer is Rs. 9632:
\[ 0.44X + (0.45X + 1800) = 9632 \]

### Step 5: Simplify the equation
Combine like terms:
\[ 0.44X + 0.45X + 1800 = 9632 \]
\[ 0.89X + 1800 = 9632 \]

### Step 6: Solve for \( X \)
Subtract 1800 from both sides:
\[ 0.89X = 9632 - 1800 \]
\[ 0.89X = 7832 \]
Now, divide both sides by 0.89:
\[ X = \frac{7832}{0.89} \approx 8800 \]

### Step 7: Find the amount invested by Veer
Since Veer invested \( X + 4000 \):
\[ \text{Amount invested by Veer} = 8800 + 4000 = 12800 \]

### Final Answer
The amount invested by Veer is Rs. 12800.

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