Profit and Loss Questions

FACTS  AND  FORMULAE  FOR  PROFIT  AND  LOSS  QUESTIONS

Selling Price (SP) : The price at which the shopkeeper sells the goods is called the selling price (SP) of the goods sold by the shopkeeper.

Profit : If the selling price of an article is more than its cost price, then the dealer (or shopkeeper) makes a profit (or gain)

i.e Profit = SP - CP;       SP > CP

Loss : If the selling price of an article is less than its cost price, then the dealer suffers a loss.

i.e loss = CP - SP;        CP > SP

IMPORTANT FORMULAE

1. Profit percentage = $\left(\frac{Profit}{C.P}\times 100\right)$

2. Loss percentage = $\left(\frac{Loss}{C.P}\times 100\right)$

3.$S.P=\left[\frac{100+Gain \%}{100}\times C.P\right] = \left[\frac{100-Loss\%}{100}\times C.P\right]$

4. $C.P=\left[\frac{100}{100+Gain \%}\times S.P\right] = \left[\frac{100}{100-Loss \%}\times S.P\right]$ 

5. If an article is sold at a gain of say 35%, then SP = 135% of CP

6. If an article is sold at a loss of say 35%, then SP = 65% of CP

7. 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 :$Loss \% =\left(\frac{Common Loss and Gain \%}{10}\right){ }^2={\left(\frac{x}{10}\right)}^2$

8. If a trader Professes to sell his goods at cost price, but uses false weihts, then 

$Gain \% =\left[\frac{Error}{True Value - Error}\times 100\right]\%$