# Profit and loss

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Cost Price– the price of which an article is purchased is called its cost price(CP)
Selling Price– the price at which on 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% than the seller always increase a 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