A man invested an amount in two schemes in the ratio of 2 : 3 at the rate of 20% p.a. and 10% p.a. on compound interest respectively. If the man gets a total interest of Rs. 1208 after two years from both the schemes, the find amount invested by man?

Options

A. 6000 Rs.
B. 4800 Rs.
C. 5000 Rs.
D. 4000 Rs.

Answer

To solve the problem step by step, we need to find the total amount invested by the man in two schemes based on the given conditions.

### Step 1: Understand the Investment Ratio
The man invests in two schemes in the ratio of 2:3. Let's denote the amounts invested in the two schemes as:
- Scheme A (20% p.a.): 2x
- Scheme B (10% p.a.): 3x

### Step 2: Calculate Total Investment
The total investment can be expressed as:
\[ \text{Total Investment} = 2x + 3x = 5x \]

### Step 3: Calculate the Effective Interest Rates
For compound interest, the effective interest rate for two years can be calculated using the formula:
\[ \text{Effective Interest Rate} = r + \frac{r^2}{100} \]

- For Scheme A (20% p.a.):
\[ \text{Effective Interest Rate for A} = 20 + \frac{20^2}{100} = 20 + 4 = 24\% \]

- For Scheme B (10% p.a.):
\[ \text{Effective Interest Rate for B} = 10 + \frac{10^2}{100} = 10 + 1 = 11\% \]

### Step 4: Calculate Total Interest Earned
Next, we calculate the interest earned from each scheme after 2 years.

- Interest from Scheme A:
\[ \text{Interest from A} = \frac{24}{100} \times 2x = 0.48x \]

- Interest from Scheme B:
\[ \text{Interest from B} = \frac{11}{100} \times 3x = 0.33x \]

### Step 5: Set Up the Equation
The total interest earned from both schemes is given as Rs. 1208. Therefore, we can set up the equation:
\[ 0.48x + 0.33x = 1208 \]

### Step 6: Solve for x
Combine the terms:
\[ 0.81x = 1208 \]
Now, solve for \(x\):
\[ x = \frac{1208}{0.81} \approx 1485.19 \]

### Step 7: Calculate Total Investment
Now, substitute \(x\) back into the total investment formula:
\[ \text{Total Investment} = 5x = 5 \times 1485.19 \approx 7426 \]

### Step 8: Final Calculation
To find the exact amounts invested in each scheme:
- Amount in Scheme A:
\[ 2x = 2 \times 1485.19 \approx 2970.38 \]
- Amount in Scheme B:
\[ 3x = 3 \times 1485.19 \approx 4455.57 \]

### Conclusion
The total amount invested by the man is approximately Rs. 7426.