A shopkeeper earns a profit of 15% after selling a book at 20% discount on the printed price. The ratio of the cost price and printed price of the book is?
Question
A shopkeeper earns a profit of 15% after selling a book at 20% discount on the printed price. The ratio of the cost price and printed price of the book is?
Solution
Let's denote the cost price of the book as CP and the printed price as PP.
Step 1: We know that the shopkeeper sells the book at a 20% discount on the printed price. This means the selling price (SP) of the book is 80% of the printed price. We can express this as: SP = 0.8 * PP.
Step 2: We also know that the shopkeeper earns a profit of 15% on the cost price. This means the selling price is 115% of the cost price. We can express this as: SP = 1.15 * CP.
Step 3: Since both expressions are equal to the selling price, we can set them equal to each other: 0.8 * PP = 1.15 * CP.
Step 4: To find the ratio of the cost price to the printed price, we can rearrange this equation to solve for CP/PP: CP/PP = 0.8/1.15.
Step 5: Simplify the ratio to get the final answer. The ratio of the cost price to the printed price of the book is approximately 0.6957, or 69.57%.
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