Multiple choice

A trader buys goods at a $19\%$ discount on the label price. If he wants to make a profit of $20\%$ after allowing a discount of $10\%$, by what $\%$ should his marked price be greater than the original label price?

  1. $8\%$
  2. $-3.8\%$
  3. $33.33\%$

  4. None of the above.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let label price be L and marked price be M. Cost price C = 0.81L. Selling price S = 0.9M. Profit = 20%, so S = 1.2C = 1.2 * 0.81L = 0.972L. Thus 0.9M = 0.972L, meaning M = 1.08L. The marked price is 8% greater than the label price.

AI explanation

Let the original label price be 100, making the trader's cost price 81 after a 19% discount. To make a 20% profit, his target selling price becomes 81 times 1.2, which is 97.2. He allows a 10% discount on his new marked price, so his marked price must be 97.2 divided by 0.9, resulting in 108. This marked price is 8% greater than the original label price.

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