Final answer:
To find the percentage by which the marked price is higher than the cost price, we set up an equation using the given discount and profit percentages, ending up with the marked price being 33.33% higher than the cost price.
Step-by-step explanation:
The question asks us to calculate the percentage by which the marked price is higher than the cost price, given that a retailer offers a 10% discount on the marked price yet still makes a 20% profit.
Let's denote the cost price as CP and the marked price as MP. The retailer is offering a 10% discount on MP, which means the selling price (SP) is 90% of MP. The problem states that the seller makes a 20% profit on CP. Therefore, SP is also 120% of CP.
We can set up the equation as follows:
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- SP = 90% of MP
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- SP = 120% of CP
Since both expressions equal SP, we can make them equal each other:
90% of MP = 120% of CP
Converting percentages into decimal form and setting up the equation:
0.9MP = 1.2CP
To find the ratio of MP to CP, we divide both sides by CP:
MP/CP = 1.2/0.9
MP/CP = 4/3
MP/CP = 1.333...
This means that the marked price is 1.333 times the cost price. To find the percentage by which MP is higher than CP, we subtract 1 from this ratio and multiply by 100:
(MP/CP - 1) × 100 = 0.333... × 100
The marked price is 33.33% higher than the cost price.