The price of Shirts at Sahara Ganj is defined as rs ( 100 + 10 x 2 ) , where x is the number of shirts. Mallika purchased 5 shirts from the above shop.In the above questions if the sister of Malliks purchased k shirts but the average price was same as that of Mallika. The value of k could be :

Options

A. a.6
B. b.4
C. c.2
D. d.none of these

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Determine the total cost of shirts purchased by Mallika.
The price of shirts is given by the formula:
\[ \text{Price} = 100 + 10x^2 \]
where \( x \) is the number of shirts.

Mallika purchased 5 shirts, so we substitute \( x = 5 \):
\[ \text{Total Cost for Mallika} = 100 + 10(5^2) = 100 + 10(25) = 100 + 250 = 350 \]

### Step 2: Calculate the average cost of shirts for Mallika.
The average cost is calculated by dividing the total cost by the number of shirts purchased:
\[ \text{Average Cost for Mallika} = \frac{\text{Total Cost}}{\text{Number of Shirts}} = \frac{350}{5} = 70 \]

### Step 3: Set up the equation for Mallika's sister's purchase.
Let \( k \) be the number of shirts purchased by Mallika's sister. The average cost for her should also be 70. Therefore, the total cost for her can be expressed as:
\[ \text{Total Cost for Sister} = 70k \]

### Step 4: Express the total cost using the price formula for \( k \) shirts.
Using the price formula for \( k \) shirts:
\[ \text{Total Cost for Sister} = 100 + 10(k^2) \]

### Step 5: Set the two expressions for total cost equal to each other.
Since both expressions represent the total cost for Mallika's sister, we can set them equal:
\[ 70k = 100 + 10k^2 \]

### Step 6: Rearrange the equation into standard quadratic form.
Rearranging gives us:
\[ 10k^2 - 70k + 100 = 0 \]
Dividing through by 10 simplifies this to:
\[ k^2 - 7k + 10 = 0 \]

### Step 7: Factor the quadratic equation.
We need to factor the quadratic equation:
\[ k^2 - 7k + 10 = (k - 2)(k - 5) = 0 \]

### Step 8: Solve for \( k \).
Setting each factor to zero gives us:
\[ k - 2 = 0 \quad \Rightarrow \quad k = 2 \]
\[ k - 5 = 0 \quad \Rightarrow \quad k = 5 \]

### Step 9: Determine the valid value of \( k \).
The problem states that we need to find the value of \( k \) that is given in the options. Since the options provided do not include 5 but do include 2, we conclude:
\[ \text{The value of } k \text{ is } 2. \]