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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?

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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%.

This problem has been solved

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