## Profit & Loss

### Important Facts

Cost Price: The price at which an article is purchased, is called its cost price, abbreviated as C.P

Selling Price:  The price at which an article is sold is called its selling price, abbreviated as S.P

Profit or Gain: If S.P is greater than C.P, the seller is said to have a profit or gain

Loss:  If S.P is less than C.P., the seller is said to have incurred a loss.

### Important Formulae

1. Gain =(S.P) - (C.P)
2. Loss = C.P - S.P
3. Loss or gain is always reckoned on C.P
4. Gain% = $$\left(\frac{\operatorname{Gain} \times 100}{\mathrm{C.P.}}\right)$$
5. Loss% = $$\left(\frac{\operatorname{Loss} \times 100}{\mathrm{C} \cdot \mathrm{P}}\right)$$
6. S.P = $$\frac{(100+\operatorname{Gain}\%)}{100} \times \mathrm{C} \cdot \mathrm{P}$$
7. S.P = $$\frac{(100-\operatorname{Loss}\%)}{100} \times \mathrm{C} \cdot \mathrm{P}$$
8. C.P = $$\frac{100}{(100+\operatorname{Gain}\%)} \times \mathbf{S}.\mathbf{P}$$
9. C.P = $$\frac{100}{(100-\operatorname{Loss}\%)} \times \mathbf{S}.\mathbf{P}$$

### Important Formulae

• If an article is sold at a gain of say, 35 %, then SP = 135% of C.P
• If an article is sold at a loss of say, 35 %, then SP = 65% of C.P
• When a person sells two similar items, one at a gain of say, $$x^{2}$$ and the other  Loss% = $$\left(\frac{Common\, Loss \,and\, Gain\% }{10}\right) ^{2}$$  = $$\left(\frac{x}{10}\right)^{2}$$
• If a trader professes to sell his goods at cost price, bat uses false weights, then Gain% = $$\left[\frac{Error}{(True\,Value)\, -\, (Error) } \times100\right]$$ %