Formulas

Profit = S.P. –C.P.

Loss = C.P. – S.P.

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

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

Illustrative Examples

Example 1: John bought a watch for Rs 540 and sold it for Rs 585. Find his profit and profit percentage.

Solution. C.P. of the watch = Rs 540, S.P. of the watch = Rs 585

            Profit = S.P. — C.P.
                       = Rs 585 — Rs 540 = Rs 45

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

                               = (\(\frac{45}{540}\) X 100 ) %

                               =  \(\frac{100}{12}\) %                  

                               = \(\frac{25}{3}\) %
                               = \(8\frac{1}{3}\) %

Example 2: By selling a bike for Rs 22464, Ansari incurs a loss of Rs 1536. Find his loss percenta

Solution. S.P. of the bike = Rs 22464, loss = Rs 1536
            C.P. of the bike = S.P. + loss = Rs 22464 + Rs 1536 = Rs 24000

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

                             = (\(\frac{1536}{24000}\) X 100 ) %

                             =  \(\frac{1536}{240}\) %
                             = \(\frac{64}{10}\) %
                             = 6.4 %

Example 3: B ijoy bought bananas at the rate of 5 for Rs 4 and sold them at the rate of 4 for Rs 5. Calculate his gain percentage.

Solution.

                C.P. of 5 bananas = Rs 4

                C.P. of 1 banana = Rs \(\frac{4}{5}\) = Rs 0.80

                S.P. of 4 bananas = Rs 5

                S.P. of 1 banana = Rs \(\frac{5}{4}\) = Rs 1.25

    Therefore,        Gain on the sale of one banana = S.P. — C.P. = Rs 1.25 — Rs 0.80 = Rs 0.45

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

                                 = (\(\frac{0.45}{0.80}\) X 100 ) %

                                 =  \(\frac{145}{80}\) %
                                 = \(\frac{225}{4}\) %
                                 = 56.25 %