Formulas

Profit % = \(\frac{Profit}{ C.P.}\) x 100

Loss % = \(\frac{ Loss}{C.P.}\) x 100

S.P. = (\(\frac{100 + Profit \%}{ 100}\)) x C.P.

S.P. = (\(\frac{100 – Loss \%}{ 100}\)) x C.P.

Illustrative Examples

Example 1: Kirpal bought a certain number of apples at Rs 75 per score and sold them at a profit of 40%. Find the selling price per apple.

Solution. C.P. of one score i.e.,  20 apples = Rs 75, profit = 40%
          S.P. of 20 apples= ( 1 + \(\frac{40}{100}\) )of Rs 75 

                                       = Rs ( \(\frac{140}{100}\) x 75 ) = Rs 105

          S.P. of one apple = Rs \(\frac{105}{20}\)

                                       = Rs \(\frac{21}{4}\) = Rs 5.25

Example 2: Bashir bought an article for Rs 1215 and spent Rs 35 on its transportation. At what price should he sell the article to have a gain of 16%?

Solution. The effective cost price of the article is equal to the price at which it was bought plus the transportation charge.

        C.P. of the given article = Rs (1215 + 35) = Rs 1250
        Gain percent = 16%

        Gain = 16% of cost price = Rs (\(\frac{16}{100}\) x 1250) = Rs 200

        S.P. = C.P. + Gain = Rs 1250 + Rs 200 = Rs 1450

Example 3: Krishnamurti bought oranges at Rs 5 a dozen. He had to sell them at a loss of 4%. Find the selling price of one orange.

Solution. We have, C.P. of one dozen oranges = Rs 5.

                Loss percent = 4%

                Loss = 4 % of Rs 5 = Re(\(\frac{4}{100}\) x 5) = Re (\(\frac{1}{5}\))

                S.P. = C.P. — Loss = Rs (5 – \(\frac{1}{5}\)) = Rs \(\frac{24}{5}\)

            Thus, S.P. of one dozen oranges = Rs \(\frac{24}{5}\)

    Therefore, S.P.of an orange = Re (\(\frac{24}{5}\) x \(\frac{1}{12}\))
                                                     = Re \(\frac{2}{5}\)
                                                     = \(\frac{2}{5}\) x 100 paise
                                                     = 40 paise