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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