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 )
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 )
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
Or
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
Or
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
Example- Find the SP when CP is ₹ 120 and gain is 20%.
Solution:- Given, CP = ₹ 120
gain = 20%
Example- Find the selling price of an article when cost price is ₹ 75 and loss is 20 %.
Solution :- given, CP = ₹ 75
loss = 20 %
Example- Find the cost price when selling price is ₹ 200 and gain is 20 %.
Solution:- given, SP = ₹ 200
gain = 20 %
Example- Find the CP when SP is ₹ 600 and loss is 25 %.
Solution: - given, SP = ₹ 600
Loss = 25 %
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 = ?
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
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%
Trick- If the cost price of 'x' article is equal to the selling price of 'y' article, then profit percentage
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
Trick- By selling an article a shopkeeper earns x% on selling price, then actual profit percent
Example– By selling an article, a shopkeeper earns 20% on selling price. Find his actual profit percent.
Solution:- Here, x = 20 %
Trick– By selling an article a shopkeeper loss x % on selling price, then actual loss percent
Ex– By selling an article a shopkeeper loss 20 % on selling price. Find actual loss percent.
Solution:- Here, x = 20 %
Trick- If a dishonest trader professes to sell his items at cost price but uses false weight, then
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
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
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%
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
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
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.
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 %