Question

By selling an article for Rs. 240, a man incurs a loss of 10%. At what price should he sell it to make a profit of 20%?
A) Rs. 264
B) Rs. 268
C) Rs. 300
D) Rs. 320

Answer 1

Hint: For solving this question, we let the cost price of the article be x. Selling price of an article at a loss of 10 percent is given. So, by using this we easily calculate the actual cost price of the article. Using the cost of the article, we can easily find the selling price of the article at 20 percent profit.

Complete step-by-step answer:
As per given in the question the selling price of the article is Rs. 240 at 10 percent loss.
Let the cost price of the article be x rupees. Percent loss is 10, so loss price is $\dfrac{10}{100}x$.
The formula for loss can be expressed as: Cost price – percent loss price = Selling price.
Now, selling an article at 10 percent loss the selling price is Rs. 240.
$\begin{align}
  & x-\dfrac{10}{100}x=240 \\
 &\Rightarrow \dfrac{100x-10x}{100}=240 \\
 &\Rightarrow \dfrac{90}{100}x=240 \\
 &\Rightarrow x=240\times \dfrac{100}{90} \\
 &\Rightarrow x=266.67 \\
\end{align}$
The cost price of the article is Rs. 266.67.
For profit the formula can be expressed as: Cost price + profit percent price = Selling price
To gain 20 percent profit, the selling price of the article should be:
$\begin{align}
  & =266.67+\dfrac{20}{100}\times 266.67 \\
 & =266.67\times \dfrac{120}{100} \\
 & =266.67\times 1.2 \\
 & =Rs.320 \\
\end{align}$
Hence, to make a profit of 20 percent in the article the selling price should be Rs. 320.
Therefore, option (D) is correct.

Note: Students must first calculate the actual cost price of the article by using suitable formulas and should not use the price given in the problem statement directly to evaluate the profit price. In doing so, he will tick mark the wrong option.