Question : If an article is sold at $\frac{9}{10}th$ of its usual selling price, 20% profit would be made on it. Find the profit percentage which would have been made on it on selling it at its usual selling price.
Option 1: 33.33%
Option 2: 25%
Option 3: 30%
Option 4: 20%
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Correct Answer: 33.33%
Solution : Let the selling price be $100x$. The article is sold at $\frac{9}{10}$th of its usual selling price, and a 20% profit is made. Then the new selling price = $\frac{9}{10} \times 100x = 90x$ Selling price = $\frac{100+ Profit\%}{100}×$ cost price ⇒ $90x$ = $\frac{100+20}{100} \times$ cost price ⇒ Cost price = $\frac{90x\times 10}{12}$ ⇒ Cost price = $75x$ Now the article is sold at the actual price which is $100x$, so the profit percentage will be Profit% = $[\frac{SP - CP}{CP}] \times100$ $=\frac{(100x-75x)}{75x} \times 100$ $=\frac{(25x)}{75x} \times 100$ $=\frac{1}{3} × 100$ $=33.33$% Hence, the correct answer is 33.33%.
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