A shopkeeper sold an article for 2090.42 without any loss or profit. Approximately, what will be the profit percent, if he sold that article for 2602.58?
(a) $15\%$,
(b) $20\%$,
(c) $25\%$,
(d) $30\%$.

Hint: We start solving the problem by recalling the fact that there will be no profit or loss if the selling price of goods is equal to cost price, using which we get the cost price of the article. We then substitute the new selling price and the obtained cost price in the formula $profit\%=\dfrac{selling\ price-\operatorname{cost } price}{\operatorname{cost } price}\times 100$ and make necessary calculations to get the required result.

Complete step-by-step answer:
According to the problem, we are given that the shopkeeper sold an article for 2090.42 without any loss or profit. We need to find the profit percent, if he sold that article for 2602.58.
According to the problem, we have a selling price of 2090.42 at which we get neither profit nor loss. We know that there will be no profit or loss if the selling price of goods is equal to the cost price. Using this fact, we get the cost price of the article as 2090.42.
Now, we need to find the profit percent if the article is sold for 2602.58. So, we have the new selling price as 2602.58.
We know that the profit percent is defined as $profit\%=\dfrac{selling\ price-\operatorname{cost } price}{\operatorname{cost } price}\times 100$.
Now, let us substitute the values in this profit\%.
So, we get $profit\%=\dfrac{2602.58-2090.42}{2090.42}\times 100$.
$\Rightarrow profit\%=\dfrac{512.16}{2090.42}\times 100$.
$\Rightarrow profit\%=0.245\times 100$.
$\Rightarrow profit\%=24.5\%\approx 25\%$.
We have found the profit percent approximately as $25\%$.
∴ The profit percent if the shopkeeper sold the article for 2602.58 is $25\%$.

So, the correct answer is “Option (c)”.

Note: We should know that profit or loss percentage is calculated with respect to the cost price. We need to find the approximate profit percent which means the nearest integer value for the profit percentage. We can see 24.5 is nearer to 25 than any other numbers given in the options. We can also find the total profit made by the shopkeeper if he sells by the shopkeeper at 2602.58.