The cost price of a book is Rs. 720 and it is sold at the profit of P%. If the cost price and the selling price are interchanged, the loss incurred is L%. L is 20% less than that by P. Which of the following statement/s is/are true? I: The selling price of the book if the shopkeeper wants to earn the profit of (L +

Solution

Cost price of the book = Rs. 720 Selling price of the book = Rs. 720 × (100 + P)% = Rs. (720 + 7.2P) Profit on the book = 720 + 7.2P – 720 = Rs. 7.2P Profit percentage (P%) = (7.2P/720) × 100 After interchanging the cost price and Selling price, Cost price of the book = Rs. (720 + 7.2P) Selling price of the book = Rs. 720 Loss on the book = Rs. (720 + 7.2P) – 720 = Rs. 7.2P Loss percentage (L%) = [7.2P/(720 + 7.2P)] × 100 Ratio of L to P = 80:100 = 4:5 {[7.2P/(720 + 7.2P)] × 100}:[(7.2P/720) × 100] = 4:5 720 × 5 = 4 × (720 + 7.2P) 3600 = 2880 + 28.8P 720 = 28.8P P = 25 L = [7.2 × 25/(720 + 7.2 × 25)] × 100 = (180/900) × 100 = 20 For I: The selling price of the book if the shopkeeper wants to earn the profit of (L + P)%, is Rs. 1044. (L + P)% = (20 + 25)% = 45% Selling price of the book = Rs. 720 × 145% = Rs. 1044 Therefore, this statement is true. For II: If the marked price of the book is 2P% more than that of cost price and L% of discount is given, the selling price of the book will be Rs. 864. Marked price of the book = 720 × (100 + 50)% = Rs. 1080 Selling price of the book = 1080 × 80% = Rs. 864. Therefore, this statement is true. For III: If the ratio of the cost price to selling price of the book is 10:7, the loss on the book will be (P + 10)%. Cost price of the book = Rs. 720 Selling price of the book = (720/10) × 7 = Rs. 504 Loss on the book = 720 – 504 = Rs. 216 Loss percentage = (216/720) × 100 = 30% So, (P + 10)% = 25 + 10 = 35% Therefore, this statement is not true.