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

**Q.1 What do you mean by profit and loss?**

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.

**Q.2 What is the formula of profit and loss?**

**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.

**Q.3 What is the meaning of P&L?**

**Ans.** (P&L) statement is a financial statement that summarizes the revenues, costs, and

expenses incurred during a specified period.

**Q.4 What is profit formula?**

**Ans.** In its simplest form, the profit equation is: Profit = Revenue – Cost.

**Q.5 What is the formula of loss?**

**Ans.** Loss = C.P. – S.P. (C.P.> S.P.)

**Q.6 What is CP formula?**

**Ans.** Cost Price = Selling Price – Profit.

**Q.7 What is profit percentage?**

**Ans.** Profit percentage = (Profit/Cost Price) × 100.

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