Cost price:
The price at which the goods are or have been bought is called Cost Price and it is abbreviated as C.P.
Selling Price:
The Price at whcih the goods are or have been sold is called Selling Price and it is abbreviated as S.P.
Profit Or Gain:
If S.P. > C.P. then its a profit or gain.
Loss:
If S.P.< C.P. then its a loss.
1) Gain $=(S.P)-(C.P.)$
2) Loss $=(C.P)-(S.P)$
3) Loss or gain is always calculated on C.P.
4) Gain% $=\left(\frac{Gain\times 100}{C.P.}\right)$
5) Loss% $= \left(\frac{Loss\times 100}{C.P.}\right)$
6) S.P $= \frac{100+Gain\%}{100}\times C.P$
7) S.P $= \frac{100-Loss\%}{100}\times C.P$
8) C.P $=\frac{100}{(100+Gain\%)}\times S.P$
9) C.P $=\frac{100}{(100-Loss\%)}\times S.P$
10) If an article is sold at a gain of 25%, then S.P = 125% of C.P.
11) If an article is sold at loss of 25%, then S.P = 75% of C.P.
12) When a man sells two similar goods, one at a gain of x%, and the other at a loss of x%, then the seller always incurs a loss given by
Loss% $=\left(\frac{Common\quad Loss\quad and\quad Gain\%}{10}\right)^{2}$
$=\left(\frac{x}{10}\right)^{2}$
13) If a seller professes his goods at C.P., but uses false weights, then
Gain% $=\left[\frac{Error}{(True\quad Value)-(Error)}\times 100\right]%$.
