A trader gains $15\%$ after selling an item at $10\%$ discount on the printed price. The ratio of the cost price and the printed price is

Let the printed price be 100. Using the selling price formula after discount, Selling Price = Printed Price - (10% of 100), so the selling price is 90. Because this yields a 15% profit, the cost price is 90 / 1.15, which equals 1800 / 23, making the cost price in ratio terms 1800/23 to 100. Multiplying both sides by 23 gives a ratio of 1800 to 2300, which simplifies by dividing by 100 to 18 to 23. The ratio of the cost price to the printed price is 18:23.

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