# Profit and Loss

Profit and Loss formula is used in mathematics to determine the price of a commodity in the market and understand how profitable a business is. 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. The important terms covered here are cost price, fixed, variable and 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.

## 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 Formulas

Now let us find the profit formula and loss formula.

• The profit or gain is equal to the selling price minus the cost price.
• Loss is equal to the cost price minus the selling price.
 Profit or Gain = Selling price – Cost Price Loss = Cost Price – Selling Price

The formula for the profit and loss percentage is:

 Profit percentage (P%) = (Profit /Cost Price) x 100 Loss percentage (L%) = (Loss / Cost price) x 100

## Profit and Loss Examples

• If a shopkeeper brings a cloth for Rs.100 and sells it for Rs.120, he has made a profit of Rs.20/-.
• If a salesperson has bought a textile material for Rs.300 and has to sell it for Rs.250/-, he has gone through a loss of Rs.50/-.
• Suppose Ram brings a football for Rs. 500/- and sells it to his friend for Rs. 600/-, then Ram has made a profit of Rs.100 with a gain percentage of 20%.

These are some common examples of the profit and loss concept in real life, which we observe regularly.

## Profit and Loss Tricks

You have learned until now how to calculate profit, loss, and percentage of them. Now let us learn some tricks or formulas to solve maths problems based on gain and loss.

1. Profit, P = SP – CP; SP>CP
2. Loss, L = CP – SP; CP>SP
3. P% = (P/CP) x 100
4. L% = (L/CP) x 100
5. SP = {(100 + P%)/100} x CP
6. SP = {(100 – L%)/100} x CP
7. CP = {100/(100 + P%)} x SP
8. CP = {100/(100 – L%)} x SP
9. Discount = MP – SP
10. SP = MP -Discount
11. For false weight, profit percentage will be P% = [(True weight – false weight)/ false weight] x 100.
12. When there are two successful profits, say m% and n%, then the net percentage profit equals to [m+n+(mn/100)]
13. When the profit is m%, and loss is n%, then the net % profit or loss will be: [m-n-(mn/100)]
14. If a product is sold at m% profit and then again sold at n% profit then the actual cost price of the product will be: CP = [100 x 100 x P/(100+m)(100+n)]. In case of loss, CP = [100 x 100 x L/(100-m)(100-n)]
15. If P% and L% are equal then, P = L and %loss = P2/100
 Points to remember: For profit, the selling price should be more than the cost price For loss, the cost price should be more than the selling price The percentage value for profit and loss is calculated in terms of cost price

Let us explain the above-given formulas with examples.

## 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

1. 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?
2. 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?
3. A dishonest dealer sells goods at a 10% loss on cost price but uses 20% less weight. Compute profit or loss percentage.

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## Frequently Asked Questions on Profit and Loss

Q1

### What is meant by profit and loss?

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.
Q2

### What is the profit and loss formula?

The formula for profit = Selling price – Cost price

The formula for loss = Cost price – Selling price

Q3

### What is CP and SP in maths?

In maths, CP represents the cost price, and SP denotes the selling price.
Q4

### How is CP calculated?

CP can be calculated with the help of the formulas given below.
CP (selling price) when profit% and selling price are given:
CP = {100/(100 + P%)} x SP
CP (selling price) when loss% and selling price are given:
CP = {100/(100 – L%)} x SP
Q5

### How is SP calculated?

We can calculate the SP (selling price) using the formulas given below.
SP (selling price) when profit and cost price are given:
SP = {(100 + P%)/100} x CP
SP (selling price) when loss and cost price are given:
SP = {(100 – L%)/100} x CP
Test your Knowledge on Profit and Loss

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