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A man sold an article for Rs. $ 495 $ and gained $ 10\% $ on it. Find the cost price.

Last updated date: 28th Feb 2024
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IVSAT 2024
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Hint: The cost price is the value at which the man bought for. We are given the profit percent, we are also given the selling price of the article, as we know the relation between the cost price, selling price and the profit percent is given by the formula,
 $ CP = \dfrac{{SP}}{{100 + P\% }} \times 100 $ ,
Where SP is the selling price of the article and the CP is the cost price of the article also the $ P\% $ is the profit percent of the article. We will use this formula and plug the relevant values in the formula to get our value of cost price.

Complete step-by-step answer:
We are given the following values in the question,
Selling price of the article is given as,
 $ SP = 495 $
We are also given the profit percent which is $ 10\% $ .
We will now use the formula to get the value of the cost price,
 $ CP = \dfrac{{SP}}{{100 + P\% }} \times 100 $
Using this formula we get as,
 $ CP = \dfrac{{495}}{{100 + 10}} \times 100 $
Upon simplifying this we get,
 $ CP = \dfrac{{495}}{{110}} \times 100 $
Solving it further we get,
 $ CP = \dfrac{{4950}}{{11}} $
Solving which we get value of cost price as,
 $ CP = 450 $
Thus the value of the cost price of the given article is, $ Rs{\text{ 450}} $
So, the correct answer is “ $ Rs{\text{ 450}} $ ”.

Note: In the case that loss percent was given in the question instead of the profit percent given in this question the formula we used would have been changed as follows,
 $ CP = \dfrac{{SP}}{{100 - L\% }} \times 100 $
Where $ L\% $ is the loss percent on the article, $ CP $ is the cost price of the article and the $ SP $ is the selling price of the article.