Concept and applications of Profit and Loss
Cost Price: The price at which a particular article is bought is called its cost price (C.P.).
Selling Price: Selling price (S.P.) is that at which a particular article is sold.
Profit: If S.P. is more than C.P., then there is profit
SP >CP, (Selling price is greater than Cost Price)
Profit = (SP - CP)
Loss: If SP is less than CP then there has been a loss occurred.
SP Loss =(CP-SP)
Important formula
1. Profit = (SP - CP)
2. SP = (Profit + CP)
3. CP = (SP - Profit)
4. % Profit = $$\left( {\frac{{{\text{Profit}} \times 100}}{{{\text{CP}}}}} \right)$$
5. SP = $$\left[ {{\text{CP}} \times \left( {1 + \frac{{\% {\text{Profit}}}}{{100}}} \right)} \right]$$
6. CP = $$\left( {\frac{{100 \times {\text{SP}}}}{{100 \times \% {\text{Profit}}}}} \right)$$
7. Loss = (CP - SP)
8. SP = (CP - Loss)
9. CP = (SP + Loss)
10. %Loss = $$\left( {\frac{{{\text{Loss}} \times 100}}{{{\text{CP}}}}} \right)$$
Profit calculation on the basis of Equating the amount Spent and the Amount Earned
Profit or loss can only be calculated in case of the number of items being bought and sold being equal. We take the difference of the money got and money given to get the calculation of the profit or loss in transaction. We also calculate profit when money is equated in terms of Goods left in such case,
% profit = $$\frac{{{\text{Goods}}\,{\text{left}}}}{{{\text{Goods}}\,{\text{sold}}}} \times 100$$
Example:
A fruit vendor recovers the cost of 25 mangoes by selling 20 mangoes. Find his profit.
Solution:
$$\eqalign{
& \% {\text{Profit}} = \frac{{{\text{Goods}}\,{\text{left}}}}{{{\text{Goods}}\,{\text{sold}}}} \times 100 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5 \times \frac{{100}}{{20}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 25\% \cr} $$
Concept of Mark Up:
Traders, while selling goods, add certain percentage on the cost price. This addition is called percentage mark up, and the price thus obtained is called as marked price.
The operative relationship is:
CP + Mark Up = Marked Price
CP + %Mark Up on CP = Marked Price
Marked Price - % discount = Selling Price
Relation between CP and SP on the basis of Net percentage changes:
Suppose the SP is 25% greater than the CP. This relationship can be seen as,
CP (100) ==25%↑==>SP (125).
Solved Examples:
Example 1:
Find the single discount to equal three consecutive discounts of 10%, 12%, and 5%.
Solution:
The single discount can be given by,
100 ==12%↓==>88==5%↓==>83.6==10%↓==>75.24. (We can change percentage in any order)
Hence, single discount= (100-75.24)=24.76.
Example 2:
A shopkeeper sells two items at the same price. If he sells one of them at a profit of 10% and the other at a loss of 10%, find the percentage profit or loss.
Solution:
Such case can be solved by,
100==10 %↑( profit)==>110==10%↓(loss)==>99.
1 % loss is incurred.
Example 3:
If by selling 2 items for Rs. 180 each the shopkeeper gains 20% on one and losses 20% on the other, find the value of loss.
Solution:
100==20 %↑(profit) ==>110---20 %↓(loss) ==>96.
4% loss incurred.
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