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

### Concept & Total Cost Inclusion When a free item is given with a purchase, the Cost Price to the shopkeeper must include the cost of both the main item and the free item to accurately calculate the overall profit. ### Step-by-Step Solution - Marked Price (MP) of the racket = Rs. 30. - Discount given on racket = $15\%$. - Selling Price (SP) of the racket = $30 - (15\% \text{ of } 30) = 30 - 4.50 = \text{Rs. } 25.50$. - The customer pays Rs. 25.50 in total. This is the shopkeeper's total revenue. - Let the Cost Price (CP) of the racket be $x$. - The shopkeeper gives a free shuttlecock costing Rs. 1.50. - Total Cost Price for the shopkeeper = CP of racket + Cost of shuttlecock = $x + 1.50$. - The shopkeeper makes an overall profit of $20\%$ on his total investment. - $\text{Total Revenue (SP)} = \text{Total Cost} \times (1 + \frac{\text{Profit}\%}{100})$. - $25.50 = (x + 1.50) \times 1.20$. - $25.50 = 1.20x + (1.50 \times 1.20)$. - $25.50 = 1.20x + 1.80$. - $1.20x = 25.50 - 1.80 = 23.70$. - $x = \frac{23.70}{1.20} = \frac{237}{12} = 19.75$. - The cost price of the racket itself ($x$) is Rs. 19.75. ### Exam Strategy & Shortcut Calculate Total Revenue: $30 \times 0.85 = 25.50$. Calculate Total Cost: Revenue / $1.2 = 25.50 / 1.2 = 21.25$. Total Cost includes the racket and the shuttlecock. CP of racket = $\text{Total Cost} - \text{Cost of shuttlecock} = 21.25 - 1.50 = 19.75$. ### Common Pitfall Failing to include the cost of the free shuttlecock in the shopkeeper's Total Cost base, or mistakenly subtracting it from the Selling Price instead of adding it to the Cost Price. ### Final Answer Therefore, the correct answer is **₹ 19.75**.