Question

By selling an article for Rs. 480 a person loses \[20%.\] For what amount should he sell it to make a profit of \[20% \]?
A. Rs. 800
B. Rs. 760
C. Rs. 720
D. Rs. 680

Answer 1

Hint: First we will fill find the cost price of the article using the formulas of loss percent and loss on any item i.e.
Loss percent \[ = \dfrac{{loss}}{{C.P.}} \times 100\]
Loss on any item \[ = C.P. - S.P.\]
Now using these formulas we will get the cost price for the article, and afterward, we will find the selling price of the article if he gains on that article with \[20% \] of gain-per cent using the formula,
The gain percent $ = \dfrac{{profit}}{{C.P.}} \times 100$

Complete step by step answer:

Given data: The selling price of an article \[ = \] Rs 480
Loss percent \[ = 20\% \]
We know that loss percent \[ = \dfrac{{loss}}{{C.P.}} \times 100\]
And loss on any item \[ = C.P. - S.P.\]
Therefore, substituting the value of loss in loss percent formula
The loss percent \[ = \dfrac{{C.P. - S.P.}}{{C.P.}} \times 100\]
Now, substituting the value of loss percent and selling price of the article
$ \Rightarrow 20 = \dfrac{{C.P. - 480}}{{C.P.}} \times 100$
On cross multiplication and simplification
$ \Rightarrow 20C.P. = 100C.P. - 48000$
Combining and simplifying the like terms
$ \Rightarrow 48000 = 80C.P.$
Dividing the whole equation by 80
$C.P. = 600$
Therefore the cost price of the article \[ = \]Rs 600
Now we know that the gain percent $ = \dfrac{{profit}}{{C.P.}} \times 100$
Now if the gain percent $ = 20% $
$ \Rightarrow 20 = \dfrac{{profit}}{{600}} \times 100$
On simplifying we get,
$\therefore profit = 120$
We know that $profit = S.P. - C.P.$
$ \Rightarrow 120 = S.P. - 600$
Adding 600 on both sides
$ \Rightarrow S.P. = 720$
Therefore if the person sells the article of Rs. 720 then he would have a gain-percent of \[20% \]
Option (C) is correct.

Note: Most of the students while writing the formula for loss percent, take selling price in the denominator which is not correct as it should be the cost price that is the main reference, so while writing formulas like this we should remember all the terms to apply them correctly. Similarly, while applying the formula for gain percent the same mistake is there, so always keep it in mind that the main reference should be taken the cost price of the article and not the selling price of the article.