Question : The marked price of an article is 40% above its cost price. If its selling price is $73 \frac{1}{2} \%$ of the marked price, then the percentage profit is:
Option 1: 2.9%
Option 2: 2.7%
Option 3: 2.6%
Option 4: 2.5%
Correct Answer: 2.9%
Solution :
Let the cost price of the article be $100$.
Then marked price of the article is $(100 + 40) = 140$
Selling price is $73 \frac{1}{2}\%$ of the marked price
= $\frac{147}2\%$ of the marked price
= ${140 × (\frac{147}2)}\times \frac{1}{100}$
= $ \frac{(140 × 147)}{200} = 102.9$
Now, Profit percentage = $\frac{\text{Selling Price - Cost Price}}{\text{Cost Price}}\times 100\%.$
⇒ Profit percentage = $\frac{102.9 - 100}{100}\times 100\%$.
⇒ Profit percentage = 2.9%
Hence, the correct answer is 2.9%.
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