# A person sold an article for Rs.230 and incurred a loss of 8%. What should be the selling price in order to earn a profit of 8%?

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Hint: In this question, we will first calculate the actual cost price of the article, since it is being sold at a loss so, C.P would be more than Rs. 230 and then with that Cost price we will find out the new selling price with profit of 8% which is the required answer.

It is given that the selling price (S.P) of the article = Rs. 230
Loss incurred on the article is 8 %;
Now, we will find the cost price of the article using the following formula:
$$C.P = \dfrac{{100}}{{100 - loss\% }} \times S.P$$
= $$\dfrac{{100}}{{100 - 8}} \times 230$$
On solving, we get
=$$\dfrac{{100}}{{92}} \times 230$$= $$250$$
Hence, the cost price of that article was Rs. 250.
Now, we will find the new selling price of the article so that the person will get the profit of 8% this time.
Using the formula:
$$S.P = \dfrac{{100 + profit\% }}{{100}} \times C.P$$
We will put all the values in the above formula and we will get;
$$S.P = \dfrac{{100 + 8}}{{100}} \times 250$$
On solving the above equation, we get;
$$S.P = \dfrac{{108}}{{100}} \times 250$$
\eqalign{ & S.P = \dfrac{{108}}{{10}} \times 25 = \dfrac{{108}}{2} \times 5 \cr & = 54 \times 5 \cr & = 270 \cr & \cr}
Hence, we get the selling price of the article as Rs. 270, when the person incurred the profit of 8%.

Note:We will find out the original cost price of the article as loss % of 8% is given, now if we want to sell that article on profit of 8%, we will calculate the new selling price using the formula of profit %.Students should remember the formulas i.e $$C.P = \dfrac{{100}}{{100 - loss\% }} \times S.P$$ and $$S.P = \dfrac{{100 + profit\% }}{{100}} \times C.P$$ for solving these types of problems.