Kapil sells a badminton racket whose marked price is Rs 30, at a discount of 15% and gives a shuttle cock costing Rs 1.50 free with each racket. Even then he makes profit of 20%. His cost price, per racket, is

Options

A. Rs 21.00
B. Rs 21.25
C. Rs 20.00
D. Rs 19.75

Answer

To find the cost price of the badminton racket, we can follow these steps:

### Step 1: Calculate the Selling Price
The marked price of the badminton racket is Rs 30, and it is sold at a discount of 15%.

**Formula for Selling Price (SP):**
\[ SP = \text{Marked Price} - \text{Discount} \]

**Calculate the Discount:**
\[ \text{Discount} = \frac{15}{100} \times 30 = 4.5 \]

**Now, calculate the Selling Price:**
\[ SP = 30 - 4.5 = 25.5 \]

### Step 2: Calculate the Profit
Kapil makes a profit of 20%.

**Formula for Selling Price in terms of Cost Price (CP):**
\[ SP = CP + \text{Profit} \]
Where Profit = 20% of CP.

Thus, we can express it as:
\[ SP = CP + 0.2 \times CP = 1.2 \times CP \]

### Step 3: Set Up the Equation
From the above, we can set up the equation:
\[ 25.5 = 1.2 \times CP \]

### Step 4: Solve for Cost Price (CP)
Now, we can solve for CP:
\[ CP = \frac{25.5}{1.2} \]

Calculating this gives:
\[ CP = 21.25 \]

### Step 5: Adjust for the Shuttle Cock Cost
Since Kapil gives a shuttle cock costing Rs 1.50 free with each racket, we need to subtract this cost from the total cost price to find the actual cost price of the racket.

**Actual Cost Price of the Racket:**
\[ \text{Actual Cost Price} = CP - \text{Cost of Shuttle Cock} \]
\[ \text{Actual Cost Price} = 21.25 - 1.50 = 19.75 \]

### Final Answer
The cost price of the badminton racket is Rs 19.75.

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