Question : A shopkeeper earns a profit of 15% after selling a book at a 20% discount on the printed price. The ratio of the cost price to the printed price of the book is:
Option 1: 20 : 23
Option 2: 23 : 20
Option 3: 16 : 23
Option 4: 23 : 16
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Correct Answer: 16 : 23
Solution : Selling price = $\frac{100-\text{discount%}}{100}×$ marked price Selling price = $\frac{100+ \text{profit%}}{100}×$ cost price From both formulas, $\frac{100-\text{discount%}}{100}×$ marked price = $\frac{100+ \text{profit%}}{100}×$ cost price ⇒ $\frac{100-20}{100}×$ marked price = $\frac{100+15}{100}×$ cost price ⇒ Cost price : marked price = 80 : 115 = 16 : 23 Hence, the correct answer is 16 : 23.
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