A bank offers 10% p.a. at CI in scheme 'A', 20% p.a. at CI in scheme 'B' and 40% p.a. at CI in scheme 'C'. Veer have some amount in his hand. He invested 32% amount in scheme 'A', 20% in scheme 'B' and remaining in scheme 'C. After two year he received 6600 as interest. Find the difference between amount invested by Veer on scheme 'C' to that of in scheme 'B'.

Options

A. 5000
B. 4000
C. 2000
D. 3000

Answer

To solve the problem step by step, we will follow the outlined process:

### Step 1: Define the Total Amount
Let the total amount that Veer has be \( P \).

### Step 2: Calculate Investments in Each Scheme
- Amount invested in Scheme A: \( 0.32P \)
- Amount invested in Scheme B: \( 0.20P \)
- Amount invested in Scheme C: \( P - (0.32P + 0.20P) = P - 0.52P = 0.48P \)

### Step 3: Calculate the Compound Interest for Each Scheme
The formula for Compound Interest (CI) for 2 years is given by:
\[ CI = P \times \left(1 + \frac{r}{100}\right)^n - P \]
Where \( r \) is the rate of interest and \( n \) is the number of years.

#### For Scheme A (10% p.a.):
\[ CI_A = 0.32P \times \left(1 + \frac{10}{100}\right)^2 - 0.32P \]
Calculating:
\[ CI_A = 0.32P \times \left(1.1\right)^2 - 0.32P = 0.32P \times 1.21 - 0.32P = 0.3872P - 0.32P = 0.0672P \]

#### For Scheme B (20% p.a.):
\[ CI_B = 0.20P \times \left(1 + \frac{20}{100}\right)^2 - 0.20P \]
Calculating:
\[ CI_B = 0.20P \times \left(1.2\right)^2 - 0.20P = 0.20P \times 1.44 - 0.20P = 0.288P - 0.20P = 0.088P \]

#### For Scheme C (40% p.a.):
\[ CI_C = 0.48P \times \left(1 + \frac{40}{100}\right)^2 - 0.48P \]
Calculating:
\[ CI_C = 0.48P \times \left(1.4\right)^2 - 0.48P = 0.48P \times 1.96 - 0.48P = 0.9408P - 0.48P = 0.4608P \]

### Step 4: Total Interest Earned
The total interest earned from all schemes after 2 years is:
\[ Total\ Interest = CI_A + CI_B + CI_C = 0.0672P + 0.088P + 0.4608P = 0.616P \]

### Step 5: Set Up the Equation
According to the problem, the total interest received after 2 years is 6600:
\[ 0.616P = 6600 \]

### Step 6: Solve for \( P \)
\[ P = \frac{6600}{0.616} \approx 10700 \]

### Step 7: Calculate the Amounts Invested
- Amount in Scheme A: \( 0.32P = 0.32 \times 10700 = 3424 \)
- Amount in Scheme B: \( 0.20P = 0.20 \times 10700 = 2140 \)
- Amount in Scheme C: \( 0.48P = 0.48 \times 10700 = 5136 \)

### Step 8: Find the Difference Between Amounts in Scheme C and Scheme B
\[ Difference = Amount\ in\ Scheme\ C - Amount\ in\ Scheme\ B = 5136 - 2140 = 2996 \]

### Step 9: Round to Nearest Option
The closest option to 2996 is 3000.

### Final Answer
The difference between the amount invested by Veer in Scheme C and Scheme B is **3000**.

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