Varun and Kartik purchased the shares in ratio `7:9` for the cost of their basic salaries . The company gave each of them 50 shares as incentive , due to whichthe ratio changes to `9:11` .If each share cost is rs . 60 . Find the basic salary of Varun .

Options

A. A)Rs 13500
B. B)Rs 16500
C. C)Rs 21000
D. D)Rs 10500

Answer

To find Varun's basic salary, we can follow these steps:

### Step 1: Understand the Initial Ratio
Varun and Kartik purchased shares in the ratio of 7:9. This means if we let Varun's share amount be 7x and Kartik's share amount be 9x, where x is a common multiplier.

### Step 2: Determine the Total Shares Purchased
Let’s denote the total shares purchased by Varun and Kartik:
- Varun's shares = 7x
- Kartik's shares = 9x

### Step 3: Calculate the Incentive Shares
Both Varun and Kartik received an additional 50 shares each as an incentive. Therefore, after receiving the shares:
- Varun's total shares = 7x + 50
- Kartik's total shares = 9x + 50

### Step 4: Set Up the New Ratio
After receiving the incentive shares, the new ratio of Varun's shares to Kartik's shares is 9:11. We can set up the equation based on this new ratio:
\[ \frac{7x + 50}{9x + 50} = \frac{9}{11} \]

### Step 5: Cross Multiply to Solve for x
Cross multiplying gives us:
\[ 11(7x + 50) = 9(9x + 50) \]
Expanding both sides:
\[ 77x + 550 = 81x + 450 \]

### Step 6: Rearranging the Equation
Rearranging the equation to isolate x:
\[ 550 - 450 = 81x - 77x \]
\[ 100 = 4x \]
\[ x = 25 \]

### Step 7: Calculate Varun's Shares
Now substituting x back to find Varun's shares:
\[ \text{Varun's shares} = 7x = 7 \times 25 = 175 \]

### Step 8: Calculate Varun's Basic Salary
Each share costs Rs. 60, so Varun's basic salary can be calculated as:
\[ \text{Basic Salary} = \text{Number of Shares} \times \text{Cost per Share} = 175 \times 60 \]
Calculating this gives:
\[ \text{Basic Salary} = 10500 \]

### Conclusion
Thus, Varun's basic salary is Rs. 10,500.

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