Question : The cost price of 240 articles is the same as the selling price of $x$ articles. If profit is 20%, find the value of $x$.
Option 1: 200
Option 2: 210
Option 3: 180
Option 4: 240
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Correct Answer: 200
Solution : Profit percentage = $\frac{SP-CP}{CP}\times 100$ Where SP is the selling price and CP is the cost price. Cost Price of $240$ articles = Selling Price of $x$ articles As per given condition, CP × 240 = SP × $x$ (If SP is the Selling Price of 1 article and CP is the Cost Price of 1 article) ⇒ $\frac{SP}{CP}=\frac{240}{x}$ Now, ⇒ $ (\frac{SP}{CP}-1)\times 100 = 20$ ⇒ $(\frac{240}{x}-1)\times 100 = 20$ ⇒ $\frac{240-x}{x}\times 100 = 20$ ⇒ $6x = 1200$ ⇒ $x = 200$ Hence, the correct answer is 200.
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