Calculating profit and loss is very important in life so on this page we will read important chapter of math subject Profit and Loss.
In the previous post, we have shared the information about Simple Interest & Compound Interest on important chapters of Mathematics, definitely read it.
Let us now read and understand the information about Profit and Loss in detail.
What is Profit
If the Selling Price of an article is more than its Cost Price, then the Amount Received from their Difference is Called Profit.
- Profit = Selling Price – Cost Price
- Selling price = cost price + profit
- Cost price = selling price – profit
What is Loss
If the selling Price of an item is less than its cost price, then the Amount Received from the Difference is Called Loss.
loss = cost price – selling price
or selling price = cost price – loss
or cost price = selling price + loss
Profit and Loss Formula
- Profit = Selling Price – Cost Price
- Loss = cost price – selling price
- Selling Price = profit + cost price
- Selling Price = Cost Price – Loss
- Cost Price = selling price – profit
- Cost Price = loss + selling price
- Profit % = (Profit × 100)/Cost Price
- Loss % = (Loss × 100)/CP
- Selling Price = Cost Price (1 + Profit/100)
- Cost Price = Selling Price / (1 + Profit / 100)
- Selling Price = Cost Price (1 – Loss/100) Cost Price = Selling Price/(1 – Loss/100)
Percent gain or Percent Loss
The profit or loss on Rs 100 is called the Percentage profit or loss, the percentage of profit or loss is always determined on the cost price.
- Thus, percent profit = profit × 100 / cost price
- Percent loss = loss × 100 / cost price
What is Overhead?
The tax paid in buying an item and the expenses incurred in bringing it etc. are called overheads. Unless otherwise stated in the question, overheads are included in the purchase price of the item.
Profit and Loss Basic Concepts
Let us learn profit and loss concepts in maths. It is well explained in terms of cost price and selling price.
Profit (P) :- The amount gained by selling a product for more than its cost price.
Loss (L) :- The amount the seller incurs after selling the product less than its cost price is mentioned as a loss.
Cost Price (CP) :- The amount paid for a product or commodity to purchase is called a cost price. Also, denoted as CP. This cost price is further classified into two different categories:
Fixed Cost: The fixed cost is constant, it doesn’t vary under any circumstances
Variable Cost: It could vary depending on the number of units and other factors
Selling Price (SP) :- The amount for which the product is sold is called the Selling Price. It is usually denoted as SP. Also, sometimes called a sale price.
Marked Price Formula (MP) :- This is basically labelled by shopkeepers to offer a discount to the customers in such a way that,
- Discount = Marked Price – Selling Price
- And Discount Percentage = (Discount/Marked price) x 100
Profit and Loss Questions
Q.1 The cost price of an article is Rs.4000 and the selling price of that article is Rs.4200. What is the profit of the article?
A. 5% profit
B. 7% profit
C. 5% loss
D. 7% loss
Solution :- According to the question,
Profit = Selling Price – Cost Price
profit = 4200 – 4000
= 200
Profit = Profit / Cost Price × 100
200 / 4000 × 100
5% profit
Ans. 5% profit
Q.2 The cost price of a book is Rs.500 and the selling price is Rs.650, then how much money and what percent will be the profit on selling it?
A. 20%
B. 30%
C. 10%
D. 40%
Solution:- According to the question,
Profit = Selling Price – Cost Price
profit = 650 – 500
Profit = 150
Profit = Profit / Cost Price × 100
Profit = 150/500 × 100
= 30%
Ans. 30%
Q.3 Ram bought an old scooter for Rs.4700 and spent Rs.800 on its repairs. If he sells the scooter for Rs.5,800, what is his profit percent?
A. 60/11 profit
B. 68/13 profit
C. 60/11 loss
D. 63/7 loss
Solution:- According to the question,
Cost price = 4700
Selling price = 5800
= 4700 + 800
= 5500 – 5800
= 300 profit
= 300/5500 × 100
= 60/11 profit
Ans. 60/11 profit
Q.4 If the cost price of 20 articles is same as the selling price of 30 articles, then what will be the profit/loss %?
A. 50/3%
B. 200/3%
C. 100/3%
D. 221/13%
Solution:- According to the question,
30 – 20 = 10
P/L% = 10/30 × 100
= 100/3 % loss
Ans. 100/3 %
Q.5 A shopkeeper cheats 12% when he buys an article, he cheats 12% when he sells the article, then what percent of the total profit did he make?
A. 25.44
B. 22.55
C. 12.60
D. 28.90
Solution:- According to the question,
112 × 112 / 100
= 12544 / 100
= 125.44 – 100
= 25.44
Ans. 25.44
Q.6 If the selling price of two fans is the same, and one is sold at 10% loss and 5% profit, what will be the overall gain or loss percent?
A. 3.5%
B. 5.5%
C. 4.8%
D. 6.2%
Solution:- According to the question,
90×105/100
= 189/2
= 94.5 – 100
Loss = 5.5%
Ans. 5.5%
Q.7 A person sells two articles at the same price, he gains 20% on the first article and 25% on the second article, if the first article was bought for Rs.10000, then for how much did he buy the second article?
A. 2400
B. 4800
C. 9600
D. 6400
Solution : According to the question,
cost price = 100% = 10,000
120% = 10,000/100 × 120
= 12,000
Selling price = 12000 = 125
= 100 × 12000/125 = 100%
= 9600
Ans. 9600
Q.8 Ram bought an article for Rs.1000 and sold the article to Shyam with a profit of 20% Shyam sold it to Mohan with a loss of 10% For how much did Mohan buy it?
A. 1260
B. 1580
C. 1690
D. 1080
Solution : According to the question,
Price × (100+_ %) /100 × (100 +_ %) /100+ ……….
= 1000 × 120/100 × 90/100
= 1080
Ans. 1080
Q.9 Mohan bought an article for Rs.1080 and sold the article to Shyam with a profit of 20% Shyam sold it to Mohan with a loss of 10% For how much did Mohan buy it?
A. 100
B. 1000
C. 2000
D. 2003
Solution : According to the question,
= 1080 × 100/120 × 100/90
= 1000
Ans. 1000
Q.10 A person sells an article at 10% profit, if he sells it at 15% profit he gets Rs.200 more, what is the cost price of that article?
A. 1000
B. 2000
C. 3000
D. 4000
Solution : According to the question,
110% – 115% = 200
5% = 200
100% = 4000
Ans. 4000
Q.11 By selling 12 candies for Re 1, a person incurs a loss of 20%, then how many candies should be sold for Re 1 to gain 20%?
A. 2 candies
B. 5 candies
C. 8 candies
D. 10 candies
Solution : According to the question,
1/12 × 120/80
= 1/8
= 8 candies
Ans. 8 candies
Q.12 The ratio of selling price and cost price of an article is 5 : 4, what is the profit percent on selling the article?
A.25% profit
B.27% profit
C.25% loss
D.27% loss
Solution:- According to the question,
selling price = 5
cost price = 4
Profit = 1/4 × 100
Profit = 25%
Ans. 25% profit
Q.13 On selling 120 articles, a profit equal to the selling price of 30 articles is obtained. What is the profit percentage?
A. 20% profit
B. 27% profit
C. 20% loss
D. 27% loss
Solution : According to the question,
L% = y/x – y × 100
Loss % = 30/150 × 100
Loss = 20%
Ans. 20% loss
Q.14 A dishonest trader tells the customers that he sells the article at the cost price but by using wrong distribution he makes a profit of 20%. How many grams does he weigh instead of 1 kg?
A. 400/3 grams
B. 500/6 grams
C. 250/4 grams
D. 300/7 grams
Solution : According to the question,
1000gram – x gram / x gram × 100 = 20%
100 – x / x = 20/100
5(100 – x) = x
500 – 5x = x
500 = 6x
x = 500/6 grams
Ans. 500/6 grams
Q.15 Suppose a shopkeeper has bought 1 kg of apples for 100 rs. And sold it for Rs. 120 per kg. How much is the profit gained by him?
Solution : Cost Price for apples is 100 rs.
Selling Price for apples is 120 rs.
Then profit gained by shopkeeper is ; P = SP – CP
P = 120 – 100 = Rs. 20/-
Q.16 For the above example calculate the percentage of the profit gained by the shopkeeper.
Solution : We know, Profit percentage = (Profit /Cost Price) x 100
Therefore, Profit percentage = (20/100) x 100 = 20%.
Q.17 A man buys a fan for Rs. 1000 and sells it at a loss of 15%. What is the selling price of the fan?
Solution : Cost Price of the fan is Rs.1000
Loss percentage is 15%
As we know, Loss percentage = (Loss/Cost Price) x 100
15 = (Loss/1000) x 100
Therefore, Loss = 150 Rs.
As we know,
Loss = Cost Price – Selling Price
So, Selling Price = Cost Price – Loss
= 1000 – 150
Selling Price = R.850/-
Q.18 If a pen cost Rs.50 after 10% discount, then what is the actual price or marked price (MP) of the pen?
Solution :
Since, we know;
MP – D = SP
where MP is marked price, D is discount, SP is selling price.
Percentage discount, D% = D/MP x 100
⇒ D = (D% x MP)/100
Substitute value of D in above formula.
MP – (D% x MP)/100 = SP
MP x (100-D%)/100 = SP
Putting the given values in formula
MP x (100 – 10) /100 = 50
MP x (90/100) = 50MP = (50 x 100)/90
MP = Rs. 55.55/-
FAQ
Ans. The profit is the amount gained by selling an article at a price greater than its cost price. In contrast, the loss is the amount lost by selling an article for less than its cost price.
Ans. Profit = Selling Price – Cost Price.
Similarly, in the case of loss, the cost price is more than the selling price.
Loss = Cost Price – Selling Price.
Ans. (P&L) statement is a financial statement that summarizes the revenues, costs, and
expenses incurred during a specified period.
Ans. In its simplest form, the profit equation is: Profit = Revenue – Cost.
Ans. Loss = C.P. – S.P. (C.P.> S.P.)
Ans. Cost Price = Selling Price – Profit.
Ans. Profit percentage = (Profit/Cost Price) × 100.
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