Profit and loss

Cost Price– the price at which an article is purchased is called its cost price(CP)
Selling Price– the price at which an article is sold is called its selling price (SP)
Profit or Gain– if SP is greater than CP, the seller is said to have a profit.

Loss- if SP is less than CP the seller is said to have is called a loss.

Calculation

$gain = SP - CP$
$gain\% = (\frac{gain}{CP}*100)$

$loss = CP-SP$
$loss\% = (\frac{loss}{CP}*100)$

$SP = (\frac{(100+gain\%)}{100})*CP$
$SP = (\frac{(100-loss\%)}{100})*CP$

$CP = (\frac{100}{(100+gain\%)})*SP$
$CP =(\frac{100}{(100-loss\%)})*SP$

If an article is sold at a gain of say $35\%$ then
$SP = 135\% of CP$

If an article is sold at a loss of say $35\%$ than
$SP = 65\% of CP$

When a person sells two similar items one at a gain of say x% & the other at a loss of x% then the seller always increases the loss given by
$loss\% = (\frac{common loss and gain}{2})^2 = (\frac{x}{10})^2$

If a trader professes to sell his goods at cost price but uses false weight than
$gain\%= [\frac{error}{((true value)-(error)} *100]\%$

Example
If pure ghee costs Rs 100/kg after adulterating it with vegetable oil casting Rs 50/kg a profit of 20% in what ratio does he mix the two?

$Mean cost price = Rs (\frac{100}{120} ×96) = Rs. 80/kg$
Required ratio- 30:20
Oil: ghee

Caret Symbol (^) and its use