Profit and Loss UPSC

The profit and loss formula finds its application in mathematics for determining the market price of a commodity and comprehending the profitability of a business. Every product has a cost price and a selling price. Based on the values of these prices, we can calculate the profit gained or the loss incurred for a particular product. This section covers important terms such as cost price, fixed and variable costs, semi-variable cost, selling price, marked price, list price, margin, etc. Also, we will learn the profit and loss percentage formula here.

For example, for a shopkeeper, if the value of the selling price is more than the cost price of a commodity, then it is a profit and if the cost price is more than the selling price, it becomes a loss. Here, in this article, we will discuss profit as well as loss concepts along with tricks to solve problems based on it.

Basics

The price at which a person buys a product is the cost price (CP) of the product for that person.
The price at which a person sells a product is the selling price (SP) of the product for that person.
When a person is able to sell a product at a price higher than its cost price, we say that he has earned a profit. That is,
If SP > CP, the difference, SP – CP is known as the profit or gain.
Likewise, when an item is sold for a price lower than its cost price, we state that a loss has been experienced.
If, however, SP < CP, then the difference, CP – SP is called the loss.

Profit and Loss Basic Concepts

Let us learn profit and loss concepts in maths. The explanation is clear 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 seller incurs a loss when selling the product for less than its cost price.

Cost Price (CP)

The cost price represents the sum paid for the acquisition of a product or commodity. 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)

Shopkeepers essentially label this to provide customers with a discount in a manner that…

Discount = Marked Price – Selling Price
And Discount Percentage = (Discount/Marked price) x 100

Formulas

Profit = SP – CP
Loss = CP – SP
Percentage Profit = (Profit/CP) * 100
Percentage Loss = (Loss/CP) * 100
(Note: in both % profit and % loss, denominator is CP)

Solved Problems

Q. 1: 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.2: 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.3: 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.4: 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) = 50

MP = (50 x 100)/90

MP = Rs. 55.55/-

Practice Questions

A table is sold at Rs. 5060 with 10% profit. What would be the gain or loss percentage if it had been sold at Rs. 4370?
Suppose the CP of 20 pens is the same as the SP of some pens. If the profit is 25%, then what is the number of pens sold?
A dishonest dealer sells goods at a 10% loss on cost price but uses 20% less weight. Compute profit or loss percentage.