Question : An article is marked 25% above its cost price. If $x$% discount is allowed on the marked price and still there is a profit of 5.5%, then what is the value of $x$?
Option 1: 16.4
Option 2: 15.4
Option 3: 13.6
Option 4: 15.6
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Correct Answer: 15.6
Solution : Given, An article is Marked 25% above the cost price. After giving $x$% discount still makes a profit of 5.5%. We know, SP = [$\frac{100 + \text{gain percentage}}{100}$] × CP And, SP = [MP – (MP × discount percentage)] Let the cost price of the article be 100 units. According to the question, The selling price of the article is = $[\frac{100 + 5.5}{100}] × 100$ = 105.5 units The Marked price of the article is = [100 + (100 × 25%)] = 100 + 25 = 125 units Also, The selling price of the article is = 105.5 ⇒ [125 – (125 × $x$%)] = 105.5 ⇒ 125 – $\frac{5x}{4}$ = 105.5 ⇒ $\frac{5x}{4}$ = 19.5 ⇒ $x = \frac{19.5 × 4}{5}$ ⇒ $x = 15.6$ Hence, the correct answer is 15.6.
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