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# A shopkeeper buys an article for Rs 180. After allowing a discount of 10% on his marked price, he wants to earn a profit of 20%. His marked price must beA. Rs 210B. Rs 240C. Rs 270D. Rs 300

Last updated date: 20th Jun 2024
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Hint: In this question, we are going to use the formula finding the gain percentage. In solving this question, first we will find the selling price of the article. After that, we will find the marked price by using the formula of Gain% or Profit%, by putting the value of the selling price that we have found earlier. After solving the equation, we will find the answer.

Complete step by step solution:
Let us solve this question.
The question is saying that a shopkeeper has bought an article for Rs 180. He has allowed a discount on the marked price of 10%, and now he wants to earn a profit of 20%. Now, it is asking to find the marked price of the article.
So, we have given that
The cost price of an article (that is CP) is Rs 180
The profit percentage or we can say the gain is 20
And, the discount on the marked price of the article is 10%.
We have to find the marked price of the article.
So, let the marked price of the article be Rs x.
As the discount on marked price is 10% or we can say $\dfrac{\text{10}}{100}$.
Hence, we can write
Selling price or SP of the article will be $\left( \text{1-}\dfrac{\text{10}}{100} \right)\text{x=}\left( \text{1-0}\text{.1} \right)\text{x=0}\text{.9x}$
As we know that $Gain\%=\text{Profit}\%=\dfrac{SP-CP}{CP}$
So, we can write
$20\%=\dfrac{0.9x-180}{180}$
We can write the above equation as
$\Rightarrow \dfrac{20}{100}=\dfrac{0.9x-180}{180}$
We can write the above equation as
$\Rightarrow \dfrac{1}{5}=\dfrac{0.9x-180}{180}$
We can write the above equation as
$\Rightarrow \dfrac{180}{5}=0.9x-180$
We can write the above equation as
$\Rightarrow 36+180=0.9x$
We can write above equation as
$\Rightarrow 216=\dfrac{9}{10}x$
We can write the above equation as
$\Rightarrow 216\times 10=9x$
We can write the above equation as
$\Rightarrow \dfrac{2160}{9}=x$
Hence, the value of x will be 240.
Hence, the marked price of the article is Rs 240.

Hence, option B is correct.

Note:
For solving this question, we should know how to find a discount percentage so that from there we can find the discounted amount or we can say the selling price. We should know the formula of gain percentage or profit percentage. The formula for gain percentage is: $Gain\%=\text{Profit}\%=\dfrac{SP-CP}{CP}$. Always remember that whenever a number is multiplied with percentage, then it can also be written as the number divided by 100 that means we can say $x\%=\dfrac{x}{100}$.