A man buys `75, 100rs` shares paying 9 percent dividend. He buys shares at such a price that he gets 12 percent of his money. At what price did he buy the shares ?

Answer

To find the price at which the man bought the shares, we can follow these steps:

### Step 1: Calculate the total nominal value of the shares
The nominal value of each share is given as ₹100, and the man buys 75 shares.

\[ \text{Total nominal value} = \text{Number of shares} \times \text{Nominal value per share} = 75 \times 100 = ₹7500 \]

### Step 2: Calculate the dividend received
The dividend rate is given as 9%. We need to calculate the total dividend received on the total nominal value of the shares.

\[ \text{Dividend} = \text{Dividend rate} \times \text{Total nominal value} = 9\% \times 7500 = \frac{9}{100} \times 7500 = ₹675 \]

### Step 3: Set up the equation for the market price
Let the market price of each share be \( y \) rupees. Therefore, the total cost for 75 shares at market price is:

\[ \text{Total cost} = 75y \]

### Step 4: Calculate the profit on investment
The man wants to earn a profit of 12% on his investment. Thus, we can express this as:

\[ \text{Profit} = 12\% \text{ of Total cost} = 12\% \times 75y = \frac{12}{100} \times 75y = 0.12 \times 75y \]

### Step 5: Set the profit equal to the dividend
According to the problem, the profit he earns (which is the dividend) is equal to ₹675. Therefore, we can set up the equation:

\[ 0.12 \times 75y = 675 \]

### Step 6: Solve for \( y \)
Now, we can solve for \( y \):

\[ 0.12 \times 75y = 675 \]

\[ 9y = 675 \quad \text{(since } 0.12 \times 75 = 9\text{)} \]

\[ y = \frac{675}{9} = 75 \]

### Conclusion
The price at which he bought each share is ₹75.

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