A bookseller bought 100 copies of a book and marked its price at 40% above the cost price. He sold 40 books giving a discount of 10% and the remaining at a discount of 20%. What is his overall profit percentage?
Question
A bookseller bought 100 copies of a book and marked its price at 40% above the cost price. He sold 40 books giving a discount of 10% and the remaining at a discount of 20%. What is his overall profit percentage?
Solution 1
Sure, let's break it down step by step:
Step 1: Let's assume the cost price of each book is 100.
Step 2: The bookseller marked the price 40% above the cost price. So, the marked price of each book is 1 = $1.4.
Step 3: He sold 40 books at a discount of 10%. So, the selling price of each of these 40 books is 1.4 = 1.26 = $50.4.
Step 4: He sold the remaining 60 books at a discount of 20%. So, the selling price of each of these 60 books is 1.4 = 1.12 = $67.2.
Step 5: The total selling price for all 100 books is 67.2 = $117.6.
Step 6: The total profit is the total selling price minus the total cost price, which is 100 = $17.6.
Step 7: The profit percentage is the total profit divided by the total cost price, times 100%, which is (100) * 100% = 17.6%.
So, the bookseller's overall profit percentage is 17.6%.
Solution 2
Step 1: Let's assume the cost price of each book is 100.
Step 2: The bookseller marked the price 40% above the cost price. So, the marked price of each book is 1 = $1.40.
Step 3: He sold 40 books at a discount of 10%. So, the selling price of each of these 40 books is 1.40 = 1.26 = $50.4.
Step 4: He sold the remaining 60 books at a discount of 20%. So, the selling price of each of these 60 books is 1.40 = 1.12 = $67.2.
Step 5: The total selling price for all 100 books is 67.2 = $117.6.
Step 6: The overall profit is the total selling price minus the total cost price, which is 100 = $17.6.
Step 7: The overall profit percentage is (profit / total cost price) * 100%, which is (100) * 100% = 17.6%.
So, the bookseller's overall profit percentage is 17.6%.
Solution 3
Step 1: Let's assume the cost price of each book is 100.
Step 2: The bookseller marked the price 40% above the cost price. So, the marked price of each book is 1 = 140.
Step 3: He sold 40 books at a discount of 10%. So, the selling price of each of these 40 books is 1.4 = 1.26 = $50.4.
Step 4: He sold the remaining 60 books at a discount of 20%. So, the selling price of each of these 60 books is 1.4 = 1.12 = $67.2.
Step 5: The total selling price for all 100 books is 67.2 = $117.6.
Step 6: The overall profit is the total selling price minus the total cost price, which is 100 = $17.6.
Step 7: The overall profit percentage is (profit / total cost price) * 100%, which is (100) * 100% = 17.6%.
So, the bookseller's overall profit percentage is 17.6%.
Solution 4
Step 1: Let's assume the cost price of one book is 100.
Step 2: The bookseller marked the price 40% above the cost price. So, the marked price of one book is 1 = 140.
Step 3: The bookseller sold 40 books at a discount of 10%. So, the selling price of one book is 1.40 = 1.26 * 40 = $50.4.
Step 4: The bookseller sold the remaining 60 books at a discount of 20%. So, the selling price of one book is 1.40 = 1.12 * 60 = $67.2.
Step 5: The total selling price for 100 books is 67.2 = $117.6.
Step 6: The overall profit is the total selling price minus the total cost price, which is 100 = $17.6.
Step 7: The overall profit percentage is (profit / total cost price) * 100%, which is (100) * 100% = 17.6%.
So, the bookseller's overall profit percentage is 17.6%.
Solution 5
Step 1: Let's assume the cost price of one book is 100.
Step 2: The bookseller marked the price 40% above the cost price. So, the marked price of one book is 1 = 140.
Step 3: The bookseller sold 40 books at a discount of 10%. So, the selling price of one book is 1.40 = 1.26 * 40 = $50.4.
Step 4: The bookseller sold the remaining 60 books at a discount of 20%. So, the selling price of one book is 1.40 = 1.12 * 60 = $67.2.
Step 5: The total selling price for 100 books is 67.2 = $117.6.
Step 6: The profit is the total selling price minus the total cost price, which is 100 = $17.6.
Step 7: The profit percentage is the profit divided by the cost price, times 100%, which is 100 * 100% = 17.6%.
So, the bookseller's overall profit percentage is 17.6%.
Solution 6
Step 1: Let's assume the cost price of each book is 100.
Step 2: The bookseller marked the price 40% above the cost price. So, the marked price of each book is 1 = $1.40.
Step 3: He sold 40 books giving a discount of 10% on the marked price. So, the selling price of each of these 40 books is 1.40 = 1.26 = $50.4.
Step 4: He sold the remaining 60 books at a discount of 20% on the marked price. So, the selling price of each of these 60 books is 1.40 = 1.12 = $67.2.
Step 5: The total selling price for all 100 books is 67.2 = $117.6.
Step 6: The overall profit is the total selling price minus the total cost price, which is 100 = $17.6.
Step 7: The overall profit percentage is (Profit / Total Cost Price) * 100 = (100) * 100 = 17.6%.
So, the bookseller's overall profit percentage is 17.6%.
Solution 7
Step 1: Let's assume the cost price of one book is 100.
Step 2: The bookseller marked the price 40% above the cost price. So, the marked price of one book is 1 = 140.
Step 3: The bookseller sold 40 books at a discount of 10%. So, the selling price of one book is 1.4 = 1.26 * 40 = $50.4.
Step 4: The bookseller sold the remaining 60 books at a discount of 20%. So, the selling price of one book is 1.4 = 1.12 * 60 = $67.2.
Step 5: The total selling price for 100 books is 67.2 = $117.6.
Step 6: The profit is the total selling price minus the total cost price, which is 100 = $17.6.
Step 7: The profit percentage is the profit divided by the cost price, times 100%, which is 100 * 100% = 17.6%.
So, the bookseller's overall profit percentage is 17.6%.
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