Question : Two successive discounts, each of $x\%$ on the marked price of an article, are equal to a single discount of INR 331.20. If the marked price of the article is INR 920, then the value of $x$ is:
Option 1: 20%
Option 2: 15%
Option 3: 25%
Option 4: 18%
Correct Answer: 20%
Solution :
1st discount = $x\% \times 920 = 9.2x$
Amount after discount = $920 - 9.2x$
2nd discount $x\% \times(920 - 9.2x)=\frac{(920 - 9.2x)x}{100}$
According to the question,
$9.2x + \frac{(920 - 9.2x)x}{100} = 331.20$
⇒ $920x + 920x - 9.2x^2 = 33120$
⇒ $9.2x^2 - 1840x + 33120 = 0$
⇒ $x^2 - 200x + 3600 = 0$
⇒ $x^2 - 180x - 20x + 3600 = 0$
⇒ $(x - 180)(x - 20) = 0$
$\therefore x = 180$ or $x = 20$
180 is not valid as per the question
Hence, the correct answer is 20%.
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