Question

The percentage profit earned by selling an article for Rs.1920 is equal to the percentage loss incurred by selling the same article for Rs.1280. At what price should the article be sold to make a 25% profit?
\[
  (a){\text{ Rs}}{\text{.2000}} \\
  (b){\text{ Rs}}{\text{.2200}} \\
  (c){\text{ Rs}}{\text{.2400}} \\
  (d){\text{ Data inadequate}} \\
  {\text{(e) None of these}} \\
 \]

Answer 1

Hint: In this question let the cost price of the article be a variable x, profit is the selling price subtracted with the cost price whereas the loss will be the cost price subtracted with the selling price. Use this along with basic percentage evaluation to get the required.

Complete step-by-step solution -
Let the cost price of an article be Rs. x.
Selling price of an article when profit is earned is Rs. 1920 and when loss is incurred is Rs. 1280.
Now as we know that profit (P) is the difference of selling price and cost price and loss (L) is the difference of cost price and selling price.
$ \Rightarrow P = 1920 - x$
And
$ \Rightarrow L = x - 1280$
Now as we know percentage profit is the ratio of profit to cost price multiplied by 100 and percentage loss is the ratio of loss to cost price multiplied by 100.
Therefore %profit = $\dfrac{{1920 - x}}{x} \times 100$
And %loss = $\dfrac{{x - 1280}}{x} \times 100$
Now according to the question both percentages are equal.
Therefore, $\dfrac{{1920 - x}}{x} \times 100$ = $\dfrac{{x - 1280}}{x} \times 100$
Now simplify the above equation we have,
$ \Rightarrow 1920 - x = x - 1280$
$ \Rightarrow x + x = 1920 + 1280$
$ \Rightarrow 2x = 3200$
$ \Rightarrow x = \dfrac{{3200}}{2} = 1600$ Rs.
So the cost price of the article is Rs. 1600.
Now we have to find another selling price so that profit is 25%.
Let the new selling price be Rs y.
Therefore %profit = $\dfrac{{{\text{selling price}} - {\text{cost price}}}}{{{\text{cost price}}}} \times 100$

$ \Rightarrow 25 = \dfrac{{y - 1600}}{{1600}} \times 100$
$ \Rightarrow y - 1600 = 25 \times 16$
$ \Rightarrow y = 1600 + 400 = 2000$ Rs.
So the article should be sold at Rs.2000 so that the profit is 25%.
So this is the required answer.
Hence option (A) is correct.

Note: The trick point in this question was to take a new variable for a new selling price as now the profits have to be boosted to 25%. The direct formula for profit percentage which is $\dfrac{{{\text{selling price}} - {\text{cost price}}}}{{{\text{cost price}}}} \times 100$, helps establishing relations between the selling price and the cost price in terms of %.