Formula

Gain percent is measured on the cost price

Arithmetic • Profit and Loss

Formula

gain % = \frac{S - C}{C} \times 100

For a cost price

C

and a selling price

S

, the gain percent is

\frac{S - C}{C} \times 100

, always with the cost price as the base and never the selling price or the marked price.

How to use it

1Take $C = 100$ when only percentages are given; the rupee gain is then the gain percent itself.
2Keep the two bases apart: a discount is a percentage of the marked price, a gain is a percentage of the cost price.
3A negative value is a loss percent, quoted as a loss rather than as a negative gain.

An article bought for Rs.

250

is sold for Rs.

290

. What is the gain percent?

Step-by-step

1
$S - C = 290 - 250 = 40$
Why: The rupee gain comes first.
2
$\frac{40}{250} \times 100 = 16$
Why: Divide by the cost price, not by the selling price.

Answer

16%

Watch out

Dividing by

S

instead of

C

gives the margin on sales, a different figure. Percentages taken on different bases never simply add: a

25%

markup followed by a

20%

discount leaves no gain at all, not a gain of

5%

Builds on

Also known as

profit percent, gain percentage, percentage profit on cost, profit and loss