## Profit and Loss

The profit and loss statement is a financial statement that is related to trade and business. Whenever a purchased article is sold, then either profit is earned or loss is incurred.

Cost Price ( CP ):- When an article is purchased at any price, then that price is called cost price of the article.

Selling price ( SP ):- When an article is sold at any price, then that price is called selling price of the article.

Overhead Charges:- Overhead charges are the extra expenditures on purchased articles. Examples of overhead charges are rent, salary of employees, repairing cost etc.

### Basic Formulae :-

When an article sold at a price more than its cost price, then profit is earned. ( SP > CP )

Profit = Selling Price - Cost price
Profit = SP - CP

Example- A man buys an article for ₹ 500 and sells it for ₹ 1900. Find profit or loss.
Solution:- given, CP = 500
SP = 1900
Here, SP > CP
∴ Profit is earned
Profit = SP - CP
= 1900 - 500
= 1400 ₹

2. When an article sold at a price lower than its cost price, then loss is incurred. ( CP > SP )

Loss = Cost price - Selling price
Loss = CP - SP

Example- A person buys a cycle for ₹ 560 and sells it for ₹ 340. Find profit or loss.
Solution:- given, CP = 560
SP = 340
Here, CP > SP
Then loss is incurred
Loss = CP - SP
= 560 - 340
= ₹ 220

 2.Profit % = Profit × 100 Cost Price

Or

 Profit % = Profit × 100 CP

Example- A person buys a toy for ₹60 and sells it for ₹ 75. What will be his profit percent?
Solution:- given, CP = ₹60
SP = ₹ 75
Profit = SP - CP
= 75 - 60
= ₹ 15

 Profit % = Profit × 100 Cost Price

 Profit % = 15 × 100 = 25 % 60

 4. Loss % = Loss × 100 Cost Price

Or

 Loss % = Loss × 100 CP

Example- A person buys a book for ₹ 200 and sell it for ₹ 150. What will be his loss percent?
Solution:- Given, CP = ₹ 200
SP = ₹ 150
here, CP > SP
loss = CP - SP
= 200 - 150
= ₹ 50

 Loss % = Loss × 100 Cost Price

 Loss % = 50 × 100 = 25 % 200

 5. Selling Price = ( 100 + Profit%) × Cost Price 100

Example- Find the SP when CP is ₹ 120 and gain is 20%.
Solution:- Given, CP = ₹ 120
gain = 20%

 Selling Price = ( 100 + Profit%) × Cost Price 100

 Selling Price = ( 100 + 20 ) × 120 100

 Selling Price = 120 × 120 = ₹ 144 100

 6. Selling Price = ( 100 - Loss%) × Cost Price 100

Example- Find the selling price of an article when cost price is ₹ 75 and loss is 20 %.
Solution :- given, CP = ₹ 75
loss = 20 %

 Selling Price = ( 100 - Loss%) × Cost Price 100

 Selling Price = ( 100 - 20 ) × 75 100

 Selling Price = 80 × 75 = 20 x 3 = ₹ 60 100

 7. Cost Price = 100 × Selling Price ( 100 + Profit%)

Example- Find the cost price when selling price is ₹ 200 and gain is 20 %.
Solution:- given, SP = ₹ 200
gain = 20 %

 Cost Price = 100 × Selling Price ( 100 + Profit%)

 Cost Price = 100 × 200 ( 100 + 20 )

 Cost Price = 100 × 200 = 5 × 200 120 6

 Cost Price = 500 = ₹ 166.66 3

 8. Cost Price = 100 × Selling Price ( 100 - Loss%)

Example- Find the CP when SP is ₹ 600 and loss is 25 %.
Solution: - given, SP = ₹ 600
Loss = 25 %

 Cost Price = 100 × Selling Price ( 100 - Loss%)

 Cost Price = 100 × 600 ( 100 - 25 )

 Cost Price = 100 × 600 = 4 × 600 = 4 × 200 = ₹ 800 75 3

Example- By selling a watch for ₹ 1640, a man loses 20 % . At what price should he sell it to gain 10%.
Solution:- given, SP = ₹ 1640
loss = 20 %
gain = 10%
new SP = ?

 Cost Price = 100 × Selling Price ( 100 - Loss%)

 Cost Price = 100 × 1640 ( 100 - 20 )

 Cost Price = 100 × 1640 = 5 × 1640 = 5 × 410 = ₹ 2050 80 4

 Now , SP = ( 100 + Profit% ) × CP = ( 100 + 10 ) × 2050 100 100

 New SP = 110 × 2050 = 11 × 205 = ₹ 2255 100

### Some Useful Shortcut Method :-

Trick- When a person sells two similar articles, one at a profit of y% and another at a loss of y% then he always makes loss on that transaction which is given by

 Loss % = y2 % 100

Example- A man sold two radios for ₹ 500 each. On one he gains 24% and on the other he loses 24%. Find his gain or loss percent in the whole transaction.
Solution:- Here y = 24%

 Loss % = y2 % 100

 Loss % = 242 % 100

 Loss % = 576 = 5.76% 100

Trick- If the cost price of 'x' article is equal to the selling price of 'y' article, then profit percentage

 Profit % = ( x - y ) × 100 % y

Example- If the cost price of 25 articles is equal to the selling price of 20 articles, then find the profit percent.
Solution:- Let x = 25
y = 20

 Profit % = ( x - y ) × 100 % y

 Loss % = 25 - 20 × 100 % 20

 Profit % = 5 × 100 = 5 x 5 = 25% 20

Trick- By selling an article a shopkeeper earns x% on selling price, then actual profit percent

 Actual Profit % = x × 100 % ( 100 - x )

Example– By selling an article, a shopkeeper earns 20% on selling price. Find his actual profit percent.
Solution:- Here, x = 20 %

 Actual Profit % = x × 100 % ( 100 - x )

 Actual Profit % = 20 × 100 % 100 – 20

 Actual Profit % = 20 × 100 = 25% 80

Trick– By selling an article a shopkeeper loss x % on selling price, then actual loss percent

 Actual Loss % = x × 100 % ( 100 + x )

Ex– By selling an article a shopkeeper loss 20 % on selling price. Find actual loss percent.
Solution:- Here, x = 20 %

 Actual Loss % = x × 100 % ( 100 + x )

 Actual Loss % = 20 × 100 % 100 + 20

 Actual Loss % = 20 × 100 = 1 × 100 = 16.66% 120 6

Trick- If a dishonest trader professes to sell his items at cost price but uses false weight, then

 Profit % = Error × 100 % ( True value - Error )

Ex– A dishonest Shopkeeper professes to sell his goods at cost price but he uses a weight of 900 gm for 1 kg weight. Find his gain per cent.
Solution:- Here, True value = 1000 gm
Error = 100 gm

 Profit % = Error × 100 % ( True value - Error )

 Profit % = 100 × 100 % 1000 – 100

 Profit % = 100 × 100 = 100 = 11.11% 900 9

Trick- Selling price of two articles is ₹ S each. One of the article is sold at x % profit and another is sold at x % loss, then

 Actual Profit or Loss = ₹ 2Sx2 ( 1002 - x2 )

Ex– Selling price of two articles is ₹ 192 each. One is sold at 20 % profit and another is sold at 20 % loss. Find actual profit or loss in ₹
Solution:- Here, S = 192 and x = 20%

 Actual Profit or Loss = ₹ 2Sx2 ( 1002 - x2 )

 = 2 × 192 × 202 = 2 × 192 × 400 ( 1002 – 202 ) ( 10000 – 400 )

 Actual Profit or Loss = 2 × 192 × 400 = ₹ 16 9600

Trick- Cost price of some articles is given as ₹ 1 each. Now a shopkeeper earns x % profit, then number of articles to be sold for ₹ 1 each to ensure x % profit

 Number of articles sold = 100 × Number of articles buy 100 + x%

Ex– Cost price of 30 articles is ₹ 1. A shopkeeper earns 20 % profit. Find number of articles to be sold for ₹ 1
Solution:- Here, number of articles buy = 30 and x = 20

 Number of articles sold = 100 × Number of articles buy 100 + x%

 Number of articles sold = 30 × 100 = 30 × 100 = 25 ( 100 + 20 ) 120

Trick- By selling some articles for ₹ 1. A shopkeeper earns x% profit, then how many articles to be sold for ₹ 1 to earn y% profit.

Number of articles sold
 = 100 + x × 100 × Number of articles buy 100 100 + y

Ex- By selling 30 articles for ₹ 1 a shopkeeper earns 20%. Find number of articles to be sold for ₹ 1 to earn 50% profit.
Solution:- Here, No. of sold articles = 30
x = 20% and y = 50 %

 Number of articles sold = 100 + x × 100 × Number of articles buy 100 100 + y

 Number of articles sold = 100 + 20 × 100 × 30 100 100 + 50

 Number of articles sold = 30 × 120 × 100 100 150

 Number of articles sold = 30 × 6 × 2 = 24 5 3