Formulas of Profit and Loss

1. Gain = Selling Price (S.P.) - Cost Price (C.P.)

Simply the gain will be the amount which we get more than our cost price

2. Loss = Cost Price (C.P.) - Selling Price (S.P.)

Clearly we will be in loss if our selling price is less than our cost price, so we will subtract selling price from cost price to get the loss amount.

\begin{aligned}
3. & Gain\% = \left(\frac{Gain*100}{C.P.}\right) \\

4. & Loss\% = \left(\frac{Loss*100}{C.P.}\right) \\

5. & S.P. = \left(\frac{100+Gain\%}{100}\times C.P.\right) \\

6. & S.P. = \left(\frac{100-Loss\%}{100}\times C.P.\right) \\

7. & C.P. = \left(\frac{100}{100+Gain\%}\times S.P.\right) \\

8. & C.P. = \left(\frac{100}{100-Loss\%}\times S.P.\right) \\

\end{aligned}

9. If an article is sold at a gain of say 20%, then S.P. = 120% of C.P.
Means you "do not" need to first calculate 20 % of C.P. then to add it to the cost price to get the selling price.

10. If an article is sold at a loss of say, 20% then S.P. = 80% of C.P.

11. When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss given by:

\begin{aligned}
\left(\frac{x}{10}\right)^2 \\
\end{aligned}

12. If a trader professes to sell his goods at cost price, but uses false weights, then

\begin{aligned}
Gain\% = \left[\frac{Error}{\text{True value - Error}} \times 100\right] \%
\end{aligned}

Above all are the important formulas of profit and loss, which we use in some form in every question related to profit and loss. We should first give stress to remember formulas because our question practise may go in vain if we forget the key formula to be used. Good luck.