Question

On selling an article for $Rs.48$ ,a shopkeeper loses $20\%$ .In order to gain $20\%$ ,what would be the selling price?
A. $52$
B. $56$
C. $68$
D. $72$

Answer 1

In order to find out the selling price, at first, we need to find out the cost price of the article. So, to find out the cost price we will use the formula as: $CP = \dfrac{{SP \times 100}}{{100 - Loss\% }}$ .After calculating CP, we will find the SP of the article when a shopkeeper gains $20\%$ using the formula as: $SP = \dfrac{{CP \times \left( {100 + Gain\% } \right)}}{{100}}$.

Complete step by step answer:
It is given that, Selling Price of an article is $Rs.48$ and a shopkeeper loses $20\%$.
So, first of all we will the cost price of the article
By using formula of cost price i.e., $CP = \dfrac{{SP \times 100}}{{100 - Loss\% }}$
on substituting the values, we get
$CP = \dfrac{{48 \times 100}}{{100 - 20}}$
On simplification we get
$CP = \dfrac{{4800}}{{80}}$
On dividing $4800$ by $80$ we get,
$CP = 60$
$\Rightarrow CP = Rs.60$

So, the cost price of the article is $Rs.60$. As per the question, in order to gain $20\%$ profit, we have to find out the selling price of the article.So, to find out the selling price of the article,we will use the formula as:
$SP = \dfrac{{CP \times \left( {100 + Gain\% } \right)}}{{100}}$
So, on substituting the values, we get
$SP = \dfrac{{60 \times \left( {100 + 20} \right)}}{{100}}$
$\Rightarrow SP = \dfrac{{60 \times \left( {120} \right)}}{{100}}$
On simplification, we get
$\Rightarrow SP = 72$
$\therefore SP = Rs.72$
Thus, in order to gain $20\%$ profit, shopkeeper has to sell the article at a selling price of $Rs.72$

Hence, option D is the correct answer.

Note: There is an alternative way to solve this question. In order to solve this, we let the cost price of the article to be $Rs.{\text{ }}x$
And it is given that a shopkeeper loses $20\%$
So, $Loss\% = 20\%$ of the cost price
$\Rightarrow Loss = \dfrac{{20}}{{100}}x$
Now using the formula: $Loss = CP - SP$ we will find out the CP of the article.
So, on substituting values, we get
$\dfrac{{20}}{{100}}x = x - 48$
$\Rightarrow x - \dfrac{{20}}{{100}}x = 48$
Taking L.C.M, we get
$\dfrac{{100x - 20x}}{{100}} = 48$
$\Rightarrow \dfrac{{80x}}{{100}} = 48$
On simplifying it, we get
$\Rightarrow x = \dfrac{{48 \times 100}}{{80}} = 60$
So, the CP of the article is $Rs.60$
Now, a shopkeeper wants to gain $20\%$
So, he gains $20\%$ of the cost price
$\therefore {\text{ }}Gain = \dfrac{{20}}{{100}} \times 60 = Rs.12$
So, using formula: $SP = Gain + CP$ we get
$SP = 12 + 60 = Rs.72$ which is the required answer.And there is a key point to remember about profit and loss concept i.e., If CP is greater than SP, then loss is seen and If SP is greater than CP, then profit is seen.