Profit and loss


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.
adulterating

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