The ratio of cost price to the market price of an article is 4: 5. What is the…
2026
The ratio of cost price to the market price of an article is 4: 5. What is the profit percentage if the ratio of the profit percentage on selling the article to the discount allowed on it is 5: 4?
- A.
10%
- B.
12%
- C.
12.5%
- D.
15%
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Correct answer: C
Given: cost price : market price = 4 : 5, and profit% : discount% = 5 : 4.
Let cost price = 4x and market price = 5x. Let profit% = 5y and discount% = 4y.
Selling price (from cost price) = 4x * (100 + 5y)/100. Selling price (from market price) = 5x * (100 - 4y)/100. These are equal.
Equate and simplify: 4(100 + 5y) = 5(100 - 4y).
Expand: 400 + 20y = 500 - 20y.
Solve for y: 40y = 100 ⇒ y = 2.5.
Profit% = 5y = 5 × 2.5 = 12.5%.
Answer: The profit percentage is 12.5%.