Multiple choice

A merchant buys goods at $25$% off the list price. He desires to mark the goods so that he can given a discount of $20$% on the marked price and still clear a profit of $25$% on the selling price. What per cent of the list price must be mark the goods?

  1. $125$%
  2. $100$%
  3. $120$%
  4. $80$%
  5. $75$%
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A Correct answer
Explanation

Let list price be 100. Cost price is 75. To get 25% profit on selling price, profit = 0.25 * SP. Since SP = CP + Profit = 75 + 0.25 * SP, we get 0.75 * SP = 75, so SP = 100. Since 20% discount is given on marked price (MP), 0.8 * MP = 100, so MP = 125. Thus, 125% of list price.

AI explanation

Let the list price be 100, so the cost price for the merchant is 75 after the 25 percent discount. His desired profit is 25 percent of his selling price, which implies his cost price equals 75 percent of his selling price, making the selling price 100. He wants to give a 20 percent discount on his marked price, so the selling price represents 80 percent of the marked price. This makes the marked price 100 divided by 0.80, which equals 125, meaning he must mark the goods at 125 percent of the list price.

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