Finding The C.P. When S.P. and Profit Or Loss Percent Are Given

Formulas

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

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

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

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

Illustrative Examples

Example 1: By selling a fan for Rs 649, Anil earns a profit of 18%. Find its cost price.

Solution. S.P. of the fan = Rs 649, profit = 18%

Therefore, Rs 649 = ( 1 + \(\frac{18}{100}\)) of C.P.

=> Rs 649 = \(\frac{118}{100}\) of C.P.

=>  C.P. = Rs (649 x \(\frac{100}{118}\)) = Rs 550
Hence the cost price of the fan = Rs 550.

Example 2: By selling a chair for Rs 391, Ali suffers a loss of 15%. Find its cost price.

Solution. S.P. of the chair = Rs 391, Loss = 15%

Therefore,    Rs 391 = ( 1- \(\frac{15}{100}\)) of C.P.

Rs 391 = \(\frac{85}{100}\) of C.P.

=>  C.P. = (Rs 391 x \(\frac{100}{85}\) )= Rs (23 x 20) = Rs 460

Hence the cost price of the chair = Rs 460.

Example 3: A man sells his scooter for Rs 18000 making a profit of 20%. How much did the scooter cost him?

Solution. Let the cost price of the scooter be Rs 100. Then, Profit = Rs 20

S.P. = C.P. + Profit = Rs 100 + Rs 20= Rs 120
Thus, if the S.P. is Rs 120, then C.P. = Rs 120 – 20 = Rs 100

If the S.P. is Rs 18000, then C.P. = Rs (\(\frac{100}{120}\) x 18000) = Rs 15000

Hence, the cost of the scooter = Rs 15000