A man invested ₹4000 in a scheme giving 20% p.a. compound interest for two year. The interest received from this scheme is 500% more than the interest on some other amount from another scheme giving 8% S.I for 4 year. Find the total amount invested in both schemes.

Options

A. ₹5,200
B. ₹5,100
C. ₹5,400
D. ₹5,450

Explanation

To solve the problem step by step, we will break it down into manageable parts.

### Step 1: Calculate the Amount from the First Scheme
The first scheme involves compound interest. The formula for the amount \( A \) after \( n \) years with principal \( P \), rate \( r \), and time \( n \) is given by:

\[ A = P \left(1 + \frac{r}{100}\right)^n \]

Given:
- Principal \( P = ₹4000 \)
- Rate \( r = 20\% \)
- Time \( n = 2 \) years

Substituting the values into the formula:

\[ A = 4000 \left(1 + \frac{20}{100}\right)^2 \]
\[ A = 4000 \left(1 + 0.2\right)^2 \]
\[ A = 4000 \left(1.2\right)^2 \]
\[ A = 4000 \times 1.44 = ₹5760 \]

### Step 2: Calculate the Interest from the First Scheme
The interest \( I \) earned from the first scheme is:

\[ I = A - P \]
\[ I = 5760 - 4000 = ₹1760 \]

### Step 3: Determine the Interest from the Second Scheme
According to the problem, the interest from the first scheme is 500% more than the interest from the second scheme. Let the interest from the second scheme be \( I_2 \).

Since \( I = 500\% \) more than \( I_2 \):

\[ I = I_2 + 5 \times I_2 = 6 \times I_2 \]
\[ 1760 = 6 \times I_2 \]

Now, solving for \( I_2 \):

\[ I_2 = \frac{1760}{6} = ₹293.33 \]

### Step 4: Calculate the Principal for the Second Scheme
The second scheme provides simple interest. The formula for simple interest \( I \) is:

\[ I = \frac{P \times r \times t}{100} \]

Given:
- Rate \( r = 8\% \)
- Time \( t = 4 \) years

Substituting the values into the formula:

\[ 293.33 = \frac{P \times 8 \times 4}{100} \]
\[ 293.33 = \frac{32P}{100} \]
\[ 293.33 \times 100 = 32P \]
\[ 29333 = 32P \]
\[ P = \frac{29333}{32} = ₹916.03 \]

### Step 5: Calculate the Total Amount Invested
Now, we need to find the total amount invested in both schemes:

\[ \text{Total Amount} = P_1 + P_2 \]
Where:
- \( P_1 = ₹4000 \) (from the first scheme)
- \( P_2 = ₹916.03 \) (from the second scheme)

Calculating the total:

\[ \text{Total Amount} = 4000 + 916.03 = ₹4916.03 \]

### Final Answer
The total amount invested in both schemes is approximately **₹4916.03**.

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