## 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 %