P owns `2/3 `shares of a company and the rest of the shares is equally divided among Q and R. If the profit on each share increases from 5% to 7%, P earns an extra 800 rupees. The investment of R on the shares is

Options

A. Rs. 20,000
B. Rs. 15,000
C. Rs. 10,000
D. Rs. 40,000

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define the total shares
Let the total shares of the company be represented by \( x \).

### Step 2: Calculate P's shares
P owns \( \frac{2}{3} \) of the total shares. Therefore, P's shares can be calculated as:
\[ \text{P's shares} = \frac{2}{3} \times x = \frac{2x}{3} \]

### Step 3: Calculate the remaining shares
The remaining shares, which are owned by Q and R, can be calculated as:
\[ \text{Remaining shares} = x - \frac{2x}{3} = \frac{3x}{3} - \frac{2x}{3} = \frac{x}{3} \]

### Step 4: Divide the remaining shares between Q and R
Since the remaining shares are equally divided between Q and R, each will get:
\[ \text{Q's shares} = \text{R's shares} = \frac{1}{2} \times \frac{x}{3} = \frac{x}{6} \]

### Step 5: Calculate the profit increase for P
The profit on each share increases from 5% to 7%. The extra profit earned by P can be calculated as:
\[ \text{Extra profit} = \text{New profit} - \text{Old profit} = 7\% - 5\% = 2\% \]
Given that this extra profit amounts to Rs. 800, we can set up the equation:
\[ 2\% \text{ of P's shares} = 800 \]

### Step 6: Substitute P's shares into the equation
Substituting P's shares into the equation gives:
\[ 0.02 \times \frac{2x}{3} = 800 \]

### Step 7: Solve for \( x \)
To solve for \( x \), we can rearrange the equation:
\[ \frac{2x}{3} \times 0.02 = 800 \]
\[ \frac{2x}{3} = \frac{800}{0.02} \]
\[ \frac{2x}{3} = 40000 \]
Now, multiply both sides by \( \frac{3}{2} \):
\[ x = 40000 \times \frac{3}{2} = 60000 \]

### Step 8: Calculate R's investment
R's shares are \( \frac{x}{6} \):
\[ \text{R's shares} = \frac{60000}{6} = 10000 \]

### Final Answer
Thus, R's investment on the shares is Rs. 10,000.

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