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Price of a product is 48 units. After two successive cuts by same percentage, price of the product becomes 20.25. What is the discount percentage?

I assumed the percentage to be x and multiplied x by x/100 and x/100. Didn't get the right answer. The answer x is 10. I want to know how to get to the answer.

Curious
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    Multiplying the price by the percentage will give you the discount, not the sale price. To get the sale price, multiply the price by [1-(x/100)]. Also, if the discount really is 10% and the sale price is 20.25, the original price must have been 25, not 48. – A.J. Dec 16 '20 at 09:02
  • Your error is in what you calculated.

    $$48 \cdot \frac{x}{100} \cdot \frac{x}{100}$$

    The above quantity represents $x%$ of $x%$ of $48$. However, what is equal to $20.25$ is $x%$ removed from $x%$ again removed from $48$. That is, the correct equation is

    $$48 \cdot \frac{100-x}{100} \cdot \frac{100-x}{100} = 20.25$$

    That said, the question seems flawed as stated, since $x=10$ is not a solution to this, nor does it make sense as any other quantity I checked. But I could be missing something obvious.

     – PrincessEev Dec 16 '20 at 09:09
  • I checked. You are right. the price is 25, not 48. – Curious Dec 16 '20 at 09:28

1 Answers1

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$$48(1-x)(1-x)=20.25$$

Thus

$$x=1-\sqrt{\frac{20.25}{48}}\approx 0.35048=35.048 \%$$

tommik
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