A man invest some money party in `3%` stock at 96 and party in `4%` stock at 120. to get equal dividends from both he must invest the money in the ratio.

Options

A. `16:15`
B. `3:4`
C. `4:5`
D. `3:5`

Answer

To solve the problem of how a man should invest in two different stocks to receive equal dividends, we can follow these steps:

### Step 1: Understand the Dividend Calculation
The dividend from a stock can be calculated using the formula:
\[ \text{Dividend} = \text{Investment} \times \frac{\text{Rate of Dividend}}{100} \]
We need to ensure that the dividends from both investments are equal.

### Step 2: Set Up the Investment for Each Stock
Let’s denote:
- Investment in 3% stock as \( x \)
- Investment in 4% stock as \( y \)

### Step 3: Calculate the Dividend from Each Stock
For the 3% stock at 96:
\[ \text{Dividend from 3% stock} = x \times \frac{3}{100} \]

For the 4% stock at 120:
\[ \text{Dividend from 4% stock} = y \times \frac{4}{100} \]

### Step 4: Set the Dividends Equal
To have equal dividends from both stocks, we set the two equations equal to each other:
\[ x \times \frac{3}{100} = y \times \frac{4}{100} \]

### Step 5: Simplify the Equation
We can eliminate the fraction by multiplying both sides by 100:
\[ 3x = 4y \]

### Step 6: Express the Ratio of Investments
Rearranging the equation gives us:
\[ \frac{x}{y} = \frac{4}{3} \]
This means that the ratio of the investments in 3% stock to 4% stock is \( 4:3 \).

### Step 7: Final Ratio
To express this in a more simplified form, we can multiply both sides by a common factor. Thus, the ratio of investments can be expressed as:
\[ \text{Investment ratio} = 4:3 \]

### Conclusion
The man must invest in the ratio of \( 4:3 \) in the 3% stock and 4% stock, respectively, to receive equal dividends.

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