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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