Mr. X invested a certain amount in Debt and Equity Funds in the ratio of 4:5. At the end of one year. he earned a total dividend of 30% on his investment. After one year. he reinvested the amount including the dividend in the ratio of 6:7 in Debt and Equit Fund. If the amount reinvested in Equity Funds was ₹94.500. what was the original amount invested in Equity Funds?

Options

A. ₹75000
B. ₹81000
C. ₹60000
D. ₹ 65000

Explanation

To solve the problem step by step, we will follow the given information and perform calculations accordingly.

### Step 1: Understand the Investment Ratio
Mr. X invested in Debt and Equity Funds in the ratio of 4:5. Let's denote the amounts invested in Debt and Equity Funds as:
- Debt Fund = 4X
- Equity Fund = 5X

### Step 2: Calculate Total Investment
The total investment can be calculated as:
\[ \text{Total Investment} = 4X + 5X = 9X \]

### Step 3: Calculate the Dividend Earned
At the end of one year, Mr. X earned a total dividend of 30% on his investment. Therefore, the total amount after earning the dividend is:
\[ \text{Total Amount after Dividend} = \text{Total Investment} + \text{Dividend} \]
The dividend can be calculated as:
\[ \text{Dividend} = 30\% \text{ of Total Investment} = 0.30 \times 9X = 2.7X \]

Thus, the total amount after one year becomes:
\[ \text{Total Amount after Dividend} = 9X + 2.7X = 11.7X \]

### Step 4: Reinvesting the Amount
After one year, Mr. X reinvested the total amount including the dividend in the ratio of 6:7 (Debt Fund: Equity Fund).

### Step 5: Determine the Amount Reinvested in Equity Funds
The amount reinvested in Equity Funds is given as ₹94,500. Since the total amount is divided in the ratio of 6:7, the part of the total amount that goes into Equity Funds can be expressed as:
\[ \text{Equity Fund} = \frac{7}{6+7} \times \text{Total Amount} = \frac{7}{13} \times 11.7X \]

Setting this equal to ₹94,500 gives us:
\[ \frac{7}{13} \times 11.7X = 94,500 \]

### Step 6: Solve for X
To find X, we rearrange the equation:
\[ 11.7X = 94,500 \times \frac{13}{7} \]

Calculating the right side:
\[ 11.7X = 94,500 \times 1.8571 \]
\[ 11.7X = 175,500 \]

Now, divide both sides by 11.7:
\[ X = \frac{175,500}{11.7} \]
\[ X = 15,000 \]

### Step 7: Calculate the Original Amount Invested in Equity Funds
Now that we have the value of X, we can find the original amount invested in Equity Funds:
\[ \text{Equity Fund} = 5X = 5 \times 15,000 = 75,000 \]

### Final Answer
The original amount invested in Equity Funds was **₹75,000**.

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