Question

By selling an article for Rs. 600 a man loses 20%. At what price he will sell in order to gain 25%.
$\left( a \right)$ Rs. 600
$\left( b \right)$ Rs. 750
$\left( c \right)$ Rs. 937.50
$\left( d \right)$ Rs. 1000

Answer 1

Hint: In this particular type of question use the concept that the percentage loss is the ratio of the difference of the cost price and the selling price to the cost price multiplied by 100 so by this calculate the original cost price of an article so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given data,
Selling price of an article = Rs. 600
Let the cost price of an article be Rs. X
Now it is given that he loses 20% on an article.
So the selling price must be less than the cost price of an article.
Now as we know that the percentage loss is the ratio of the difference of the cost price and the selling price to the cost price multiplied by 100.
Therefore, 20 = \[\dfrac{{X - 600}}{X} \times 100\]
Now simplify this we have,
20X = 100X – 60000
Therefore, 80X = 60000
$ \Rightarrow X = \dfrac{{60000}}{{80}} = 750$
So the cost price of an article = Rs. 750
Now we have to find the selling price in order to gain 25%.
Let the new selling price be Rs. Y.
Now as we know that the percentage gain is the ratio of the difference of the selling price and the cost price to the cost price multiplied by 100.
Therefore, 25 = \[\dfrac{{Y - 750}}{{750}} \times 100\]
Now simplify this we have,
25(750) = 100Y - 75000
Therefore, 100Y =18750 + 75000
$ \Rightarrow Y = \dfrac{{93750}}{{100}} = 937.50$
So the new selling price of an article = Rs. 937.50
So this is the required answer.
Hence option (C) is the correct answer.

Note – Whenever we face such types of questions first find out the original cost price of an article as above then calculate the new selling price of an article as percentage gain is given by using the formula that percentage gain is the ratio of the difference of the selling price and the cost price to the cost price multiplied by 100, so simplify we will get the required answer.