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# By selling an article for Rs. 900; a man gains 20%. Find his cost price and the gain.  Hint: Use the information that, percentage profit is equal to $\dfrac{{SP - CP}}{{CP}} \times 100$, where SP stands for selling price, CP stands for cost price.

We know that, percentage profit is equal to $\dfrac{{SP - CP}}{{CP}} \times 100$. Where SP stands for selling price, CP stands for cost price. In our question selling price and percentage profit is given to us as 900 and 20% respectively. On putting the values, we get,
$\% {\text{ profit}} = \dfrac{{SP - CP}}{{CP}} \times 100 \\ \Rightarrow 20 = \dfrac{{900 - CP}}{{CP}} \times 100 \\ \Rightarrow \dfrac{{CP}}{5} + CP = 900 \\ \Rightarrow \dfrac{6}{5}CP = 900 \\ \Rightarrow CP = 900 \times \dfrac{5}{6} \\ \Rightarrow CP = 750 \\$
Hence the cost price is Rs. 750 and the gain is nothing but difference of selling price and cost price which is $900 - 750 = 150$

Note: In the profit loss question, it’s always recommended to be empathetic and this as a vendor/ person’s perspective. It’ll give us a better understanding of the question for us.
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