Profit and Loss  Formulas, Concepts and Tricks on Profit & Loss
Profit and Loss
When we buy a thing by paying some money and sell it back, then definitely we will be in either profit or loss. This profit and loss depends on selling Price and cost price.
Cost Price (C.P.):
The price, at which an article is purchased, is called its cost price, abbreviated as C.P.
Selling Price (S.P.):
The price, at which an article is sold, is called its selling prices, abbreviated as S.P.
Profit and Loss Definition:
Profit or Gain:
When selling price is more than that of cost price, then it is called profit. Formally, it can be given as
Profit = selling price(S.P.) – cost price(C.P.).
OR
If S.P. > C.P., it is a profit or gain
Loss:
When cost price is more than selling price, then it will be known as loss and it can be given as
Loss = cost price(C.P.) – selling price(S.P.).
OR
If C.P. > S.P., it is a loss.
Loss or gain is always reckoned on C.P.
Profit and Loss Formulas:
Profit (Gain) & Loss
Gain Percentage: Gain(%)
Loss Percentage: Loss(%)
In the case of a Gain or Profit,
In the case of a Loss,

If a person sells two items at the same price; one at a gain of x % and another at a loss of x %, then the seller always incurs a loss expressed as

If a trader professes to sell his goods at cost price, but uses false weights, then
Profit and Loss Problems
Example 1:
A book was purchased at 100. It was sold at 120. What is profit percent?
Solution:
C.P. = 100 and S.P. = 120. Profit = 120 ― 100 = 20.
Profit % = [(Profit/C.P.) × 100] %
Hence, gain (%) = (20/100) × 100 % = 20%
Example 2:
A boy purchased a pen at 20. He sold it his friend for 15. What is the loss he made in percentage?
Solution:
C.P. = 20 and S.P. = 15 and Loss = 20 ― 15 = 5
Loss % = [(Loss/C.P.) × 100] %
Hence, Loss (%) = (5/20) × 100 % = 25%
Example 3 :
The cost of 11 pencils is equal to the selling price of 10 pencils. Find the loss or profit percent, whatever may be the cost of 1 pencil.
Solution : The cost price of 11 pencils = S.P of 10 pencils
Let C.P of 1 pencil is 1 .
C.P of 10 pencils = 10
S.P of 10 pencils = C.P of 11 pencils = 11
Profit on 10 pencils = 11 – 10 = 1
Hence, Profit % = ( 1/ 10) x 100 = 10 %
Example 4:
Sam sold his Mobile Phone a loss of 20%. If he had sold it for 800 more, he would have received a profit of 5%. Find the cost price .
Solution :
Let the cost price be 100
So when C.P = 100 , loss of 20% means
S.P = 100 – 20 = 80
Profit of 5% means S.P = 100 + 5 = 105
The difference of two S.P = 105 – 80 = 25
If the difference is 25, C.P = 100
If the difference is $ 800 , C.P = (100 / 25 ) x 800
C.P = 3200
Hence Cost Price will be 3200
Example 5:
A reduction of20% in the price of sugar enables Mrs. Jones to buy an extra 5 kg of it for 320.
Find:
(i) the original rate, and
(ii) the reduced rate per kg.
Solution:
Let the original rate be $ x per kg.
Reduced rate = (80% of $ x) per kg
= (x × 80/100) per kg
Quantity of sugar for $ 320 at original rate = 320/x kg
Quantity of sugar for $ 320 at the new rate = 320/(4x/5) kg
= (320 × 5)/4x kg
= 400/x kg.
Therefore, (400/x) – (320/x) = 5
⇔ 5x = (400 – 300)
⇔ 5x = 80
⇔ x = 16
(i) Original rate = $ 16 per kg
(ii) Reduced rate = (4/5 × 16) per kg
= 64/5 per kg
= 12.80 per kg.
In the video Given below you will learn some better ways to calculate Profit and loss Problems