Mukesh invested a certain sum for 2 years in Scheme A offering compound interest (on an annual basis) @ `20%` pa and earned an interest of 3520. He invested the amount received from Scheme A in Scheme B offering simple interest @ `18%` for 4 years. What is the interest earned from Scheme B?

Options

A. RS... 7624.20
B. RS... 9748.40
C. RS... 8254.80
D. RS... 8294.40

Answer

To solve the problem step by step, we will first determine the principal amount Mukesh invested in Scheme A, then calculate the total amount he received after 2 years, and finally find the interest earned from Scheme B.

### Step 1: Calculate the Principal Amount in Scheme A

Given:
- Interest earned from Scheme A (I) = ₹3520
- Rate of interest (R) = 20% per annum
- Time (T) = 2 years

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

The interest earned can also be expressed as:
\[ I = A - P \]
Thus, we can rewrite the total amount \(A\) as:
\[ A = I + P \]
Substituting the formula for \(A\):
\[ I + P = P \left(1 + \frac{R}{100}\right)^T \]
Substituting the known values:
\[ 3520 + P = P \left(1 + \frac{20}{100}\right)^2 \]
\[ 3520 + P = P \left(1.2\right)^2 \]
\[ 3520 + P = P \cdot 1.44 \]

### Step 2: Rearranging the Equation

Now, rearranging the equation:
\[ 3520 = P \cdot 1.44 - P \]
\[ 3520 = P(1.44 - 1) \]
\[ 3520 = P(0.44) \]
Now, solving for \(P\):
\[ P = \frac{3520}{0.44} = 8000 \]

### Step 3: Calculate the Total Amount Received from Scheme A

Now that we have the principal amount:
\[ A = I + P = 3520 + 8000 = 11520 \]

### Step 4: Invest in Scheme B

Mukesh invests the total amount received from Scheme A into Scheme B.
- Principal for Scheme B = ₹11520
- Rate of interest (R) = 18% per annum
- Time (T) = 4 years

### Step 5: Calculate the Interest Earned from Scheme B

Using the formula for simple interest:
\[ I = \frac{P \cdot R \cdot T}{100} \]
Substituting the values:
\[ I = \frac{11520 \cdot 18 \cdot 4}{100} \]
Calculating:
\[ I = \frac{11520 \cdot 72}{100} = \frac{829440}{100} = 8294.4 \]

### Final Answer

The interest earned from Scheme B is ₹8294.4.

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