If have shares of three companies A,B and C in the ratio `2:3:4.` Company A pays `20%` divident when its Rs 250 share is availabe for Rs 310 . Company B pays `18%` divident when its Rs 100 share is available in the market for Rs 112. Company C pays `15%` divident when its Rs 50 share is available in the maket for Rs 43. If on the whole, I earn Rs 55,200 as divident from these shares, find the number of shares of each company that I have and the total market value of these shares.

Answer

To solve the problem step by step, we will follow the instructions given in the question and use the information provided about the shares and dividends.

### Step 1: Define the number of shares
Let the number of shares of companies A, B, and C be in the ratio 2:3:4. We can express the number of shares as:
- Number of shares of A = 2x
- Number of shares of B = 3x
- Number of shares of C = 4x

### Step 2: Calculate the dividends from each company
1. **For Company A:**
- Dividend = 20% of Rs 250
- Dividend per share = \( \frac{20}{100} \times 250 = 50 \)
- Total dividend from A = Number of shares × Dividend per share = \( 2x \times 50 = 100x \)

2. **For Company B:**
- Dividend = 18% of Rs 100
- Dividend per share = \( \frac{18}{100} \times 100 = 18 \)
- Total dividend from B = Number of shares × Dividend per share = \( 3x \times 18 = 54x \)

3. **For Company C:**
- Dividend = 15% of Rs 50
- Dividend per share = \( \frac{15}{100} \times 50 = 7.5 \)
- Total dividend from C = Number of shares × Dividend per share = \( 4x \times 7.5 = 30x \)

### Step 3: Set up the equation for total dividends
According to the question, the total dividend earned from all shares is Rs 55,200. Therefore, we can set up the equation:
\[ 100x + 54x + 30x = 55200 \]
\[ 184x = 55200 \]

### Step 4: Solve for x
To find the value of x, we divide both sides of the equation by 184:
\[ x = \frac{55200}{184} = 300 \]

### Step 5: Calculate the number of shares of each company
Now that we have the value of x, we can find the number of shares for each company:
- Number of shares of A = \( 2x = 2 \times 300 = 600 \)
- Number of shares of B = \( 3x = 3 \times 300 = 900 \)
- Number of shares of C = \( 4x = 4 \times 300 = 1200 \)

### Step 6: Calculate the total market value of the shares
Now, we need to calculate the total market value of the shares:
1. **Market value of shares of A:**
- Market price = Rs 310
- Total market value = Number of shares × Market price = \( 600 \times 310 = 186000 \)

2. **Market value of shares of B:**
- Market price = Rs 112
- Total market value = \( 900 \times 112 = 100800 \)

3. **Market value of shares of C:**
- Market price = Rs 43
- Total market value = \( 1200 \times 43 = 51600 \)

### Step 7: Calculate the total market value
Now, we sum up the market values of all shares:
\[ \text{Total market value} = 186000 + 100800 + 51600 = 338400 \]

### Final Answer
- Number of shares of A = 600
- Number of shares of B = 900
- Number of shares of C = 1200
- Total market value of the shares = Rs 338400