Category: Mathematics

The concept of Profit and Loss is used in our daily life, which is like we will buy some essentials goods from the shopkeeper and the shopkeeper will buy them either from the manufacturer or from wholesalers. After that, the shopkeeper will sell those goods for a higher price than they bought so that he can earn some profit.

We can see many business people follow these tactics to earn money by buying and selling goods. If the Selling Price is higher than the Actual Price or Cost Price, then he will get a profit. And if the Cost Price is higher than the Selling Price, he will get a loss. Here in this article, we will guide you on how to solve problems on Profit and Loss. In addition, you can get the Formulas for Profit and Loss along with Solved Examples.

Basics of Profit and Loss

Before stepping into the concept of Profit and Loss you need to know the fundamentals involved to calculate the Profit and Loss. They are Selling Price and Cost Price.

Cost Price(CP): Amount you usually pay to buy a product or commodity is called the Cost Price. It is in short represented as CP. In fact, CP is subdivided into two categories namely Fixed Cost and Variable Cost. The major difference between Fixed Cost and Variable Cost is that Fixed Cost remains unchanged under any circumstances whereas variable cost changes depending on the units.

Selling Price(SP): Amount for which the product is sold is referred to as Selling Price. It is represented as SP and is also called as Sale Price.

Profit: The amount gained by selling a product or commodity more than its actual price or cost price.

Loss: The Amount the Seller gets after selling a product less than its actual price.

• Calculate Profit and Profit Percent
• Calculate Loss and Loss Percent

Profit and Loss Formulas

The Formula for Profit and Loss with reference to Cost Price and Selling Price is given as such.

Profit(P)= Selling Price(SP)- Cost Price(CP)
Loss(L)= Cost Price(CP) – Selling Price(SP)
On the other hand formulas to determine the Profit %, Loss % is as such
Profit % = (Profit/Cost Price)*100
Loss % = (Loss/Cost Price)*100

Examples on Profit and Loss

1. The actual price of the book is Rs 60 and the shopkeeper sold the book for Rs 100. Find the profit that shopkeeper earned?

Solution:
The cost price of the book= Rs 60
The selling price of the book= Rs 100
Profit(P)= Selling price(SP) – Cost price (CP)
Applying the S.P and C.P of the book in the Profit Formula we have
= Rs 100 – Rs 60
= Rs 40.
Profit= Rs 40.
Therefore, Profit Gained by the Shokeeper on selling the book for 100 is Rs.40/-

2.  A man bought a cycle for Rs 5000. After a year he sold it for Rs 4000. How much did he lose?

Solution:
The cost price of the cycle= Rs 5000.
The selling price of the cycle= Rs 4000.
Substituting the Cost Price and Selling Price of the cycle we get
Loss(L)= Cost Price(CP) – Selling Price(SP).
= Rs 5000- Rs 4000
= Rs 1000.
Loss = Rs 1000.
Therefore, the man had a loss of Rs. 1000/- on selling the cycle for Rs. 4000/-.

3. Consider a Shopkeeper bought 1kg of Apples for Rs. 80 and Sold it for Rs. 100 per kg. How much is the profit gained by him?

Solution:

Cost Price of Apples = Rs. 80

Selling Price of Apples = Rs. 100

Profit = S.P – C.P

= 100 – 80

= 20

Therefore, the shopkeeper gained a profit of Rs. 20/- on selling the Apples at Rs. 100/- per Kg.

4. Calculate the Profit% gained by the Shopkeeper for the above example?

Solution:
We know Profit Percentage = (Profit/Cost Price)*100
Profit = Rs. 20/-
Apply the Profit and Cost Price Values in the Formula for Profit %
Profit % = (20/80)*100
= 25
Therefore, the shopkeeper gained a 25 % Profit Percentage.

To calculate the Loss we need to know “What is Loss?” When we sold an item or a product less than it’s actual price, then Loss occurs which means the product is sold for a low price than the actual price. Now coming to the formula to calculate Loss we have
Loss(L)= Cost Price (CP) – Selling Price(SP)

Here we can see the new terms “Selling price” and “Actual Price” or “Cost Price.” Let us discuss what they refer to.
Selling Price: The price of the product which was sold by the shopkeeper to the customer for a certain price is known as the selling price. Selling Price can also be written as SP. To calculate the Selling Price, we have a formula i.e.

Selling Price(SP)= Cost Price(CP) – Loss(L)

Cost Price: It is also called Actual Price, which means the actual cost of a product or original cost of a product or an item that was bought from the merchant or retailer. To calculate Cost Price, we have a formula i.e,
Cost Price(CP)= Selling Price(SP) + Loss(L)
In the above, we have discussed the related terms. Let’s discuss more about Loss with some examples covering every detail.

Solved Examples on Loss

1.  Find the Loss if
a) SP= 80 and CP= 100
b) SP= 120 and CP= 150
c) SP= 200 and CP= 300

Solution:

a) SP= 80 and CP= 100

We know the formula to calculate the Loss as below
Loss(L)= Cost price (CP) – Selling price(SP).
Substituting the input data in the formula and doing basic math we get
= 100- 80
= 20
Loss= 20.

b) SP= 120 and CP= 150

Formula to calculate the Loss is as under
Loss(L)= Cost price (CP) – Selling price(SP).
Apply the input data you have in the formula and perform basic math
= 150-120
= 30
Loss= 30.

c) SP= 200 and CP= 300

Formula to calculate the Loss is as below
Loss(L)= Cost price (CP) – Selling price(SP).
Substitute the input information we have to find out the Loss
= 300- 200
= 100
Loss= 100.

2. A shopkeeper bought 5 dozens bananas for Rs 300 and sold them at Rs 250. How much he loses?

Solution:
The cost price of bananas= Rs 300
The selling price of bananas= Rs 250
Formula for Loss(L)= Cost Price (CP) – Selling Price(SP).
= Rs 300- Rs 250
= Rs 50.
Loss= Rs 50.

How to Calculate the Loss Percent?

Loss percent is the percent which is expressed as the percentage of the cost price. The formula of Loss Percent is
Loss %= (Loss/ Cost Price)×100. Cost Price is always considered for reference to determine whether you got Loss or Profit. We have listed few examples explaining the process on how to find the Loss Percentage. They are as such

1.  Find Loss % if
a) SP= 80 and CP= 100
b) SP= 120 and CP= 150
c) SP= 200 and CP= 300

Solution:

a) SP= 80 and CP= 100
Formula to calculate the Loss(L)= Cost price (CP) – Selling price(SP).
= 100- 80
= 20
Loss= 20.
After finding the Loss we can determine the Loss % easily
Loss %= (Loss/ Cost Price)×100.
= (20/100) × 100
= 20%

b) SP= 120 and CP= 150
Formula to calculate the Loss(L)= Cost price (CP) – Selling price(SP).
= 150-120
= 30
Loss= 30.
Substitute the Loss value in th Loss % formula we have the equation as such
Loss%= (Loss/ Cost price)×100.
= (30/150)×100
= (1/5)×100
= 20%

c) SP= 100 and CP= 200

Apply the given input data in the formula for
Loss(L)= Cost price (CP) – Selling price(SP).
= 200- 100
= 100
Loss = 100.
Substitute the Loss in the Loss % we have the equation as such
Loss %= (Loss/ Cost Price)×100.
= (100/200)×100
= (1/2)×100
= 50.

2. A man purchased a scooter for Rs 50,000 and after two years he sold it for Rs 30,000. Find Loss and Loss percent.

Solution:

The cost price of a scooter = Rs 50,000
The selling price of a scooter= Rs 30,000
Loss(L)= Cost price (CP) – Selling Price(SP).
Substitute the input values in the formula of Loss we have
= Rs 50,000 – Rs 30,000
= Rs 20,000.

Apply the Loss in the Loss Formula we have
Loss %= (Loss/ Cost price)×100.
= (20,000/50,000)×100
= (2/5)×100
= 2×20
= 40%.

Related Articles:

• Profit and Loss
• Calculate Profit and Profit Percent

To calculate the profit we need to know “What is Profit?” The term Profit refers to the amount which we gained after selling a product. This means the “Selling price” should be more than the “Actual price” or “Cost Price.”
Now coming to the calculation of the profit we have a formula i.e

Profit(P)= Selling price(SP) – Cost Price (CP)

Here we can see the new terms “Selling Price” and “Actual Price” or “Cost Price.” Let us discuss what they refer to.

Selling Price: The price of the product which was sold by the shopkeeper to the customer for a certain price is known as the selling price. The Selling price can also be written as SP. To calculate the Selling price, we have a formula i.e.

Selling Price(SP)= Profit(P) + Cost Price(CP)

Cost Price: It is also called Actual price, which means the actual cost of a product or original cost of a product or an item that was bought from the merchant or retailer. To calculate Cost Price, we have a formula i.e,
Cost price(CP)= Selling price(SP) – Profit (P).

In the above, we have discussed the related terms. Let’s discuss more on the concept of Profit with some examples.

Solved Examples on Profit

1. Find the Profit if
a) SP= 100 and CP= 60
b) SP= 125 and CP= 100
c) SP= 90 and CP= 75

Solution:
a) SP= 100 and CP= 60
Profit(P)= Selling Price(SP) – Cost Price (CP).
= 100-60
= 40.
Profit= 40.

b) SP= 125 and CP= 100
Profit(P)= Selling Price(SP) – Cost Price (CP).
= 125-100
= 25.
Profit= 25.

c) SP= 90 and CP= 75
Profit(P)= Selling price(SP) – Cost price (CP).
= 90-75
= 15.
Profit= 15.

2. The cost price of chocolate is Rs.10 and the selling price is Rs. 15. Find the profit?

Solution:
CP of the chocolate= Rs.10
SP of the chocolate= Rs.15
Profit= Selling price(SP) – Cost price(CP).
= 15 – 10
= 5.
Profit= 5.

3. Mark bought 4 dozens of apples at $15 a dozen and sold at $20 a dozen. Find the profit?

Solution:

The cost price of apples= $15
The selling price of apples= $20
Profit(P)= Selling price(SP) – Cost price (CP).
= $20-$15
= $5.
Profit= $5.

4. Mr.Singh bought a table for Rs 15,000 and spent Rs 500 on transportation. He sold the table for Rs 17,000. Find his profit?

Solution:
Cost price of the table= Rs 15,000.
Transportation cost= Rs 500.
So, Total Cost Price= Rs 15,000+Rs 500
= Rs 15,500The selling price of the table= Rs 17,000.
Profit(P)= Selling Price(SP) – Cost Price (CP).
= Rs 17,000- Rs 15,500
= Rs 1500
Profit= Rs 1500.

Solved Examples on Selling Price

1. Find the Selling Price if
a) P= 20 and CP= 100
b) P= 32 and CP= 150
c) P= 5 and CP= 22

Solution:

a) P= 20 and CP= 100
Selling price(SP)= Profit(P) + Cost price(CP).
= 20+100
= 120.
Selling price= 120.

b) P= 32 and CP= 150
Selling price(SP)= Profit(P) + Cost price(CP).
= 32+150
= 162.
Selling price= 162.

c) P= 5 and CP= 22
Selling price(SP)= Profit(P) + Cost price(CP).
= 5+22
= 27.
Selling Price= 27.

2. The cost price of a dining set is Rs 8000 and the shopkeeper got a profit of Rs 2000. Find the selling price of the dining set?

Solution:
The cost price of the dining set= Rs 8000.
The profit that the shopkeeper got= Rs 2000.
Selling price(SP)= Profit(P) + Cost price(CP).
= Rs 2000+ Rs 8000
= Rs 10,000.
The selling price of the dining set is Rs 10,000.

Solved Examples on Cost Price

1.  Find the Cost price if
a) SP= 200 and P= 20.
b) SP= 250 and P= 50.
c) SP= 125 and P= 25.

Solution:
a)SP= 200 and P= 20.
Cost price(CP)= Selling price(SP) – Profit (P).
= 200-20.
= 180.
Cost Price= 180.

b) SP= 250 and P= 50.
Cost Price(CP)= Selling Price(SP) – Profit (P).
= 250-50
= 50.

c) SP= 125 and P= 25.
Cost price(CP)= Selling price(SP) – Profit (P).
= 125-25
= 100.

2. A shopkeeper sold a chair for Rs 2000 and he got a profit of Rs 500. What is the actual price of the chair?

Solution:
The selling price of the chair= Rs 2000.
The profit that the shopkeeper got= Rs 500.
Cost price of the chair =
Cost price(CP)= Selling price(SP) – Profit (P).
= Rs 2000- Rs 500
= Rs 1500.
So the actual price of the chair is Rs. 1500.

How to Calculate the Profit %?

The profit percentage is the percentage which is calculated with the Cost Price in the base. To calculate Profit Percent we need to know profit and cost price. The formula of profit percent is
Profit % = Profit/CP × 100.
To know how to calculate profit %, refer to the solved examples below for better understanding and solve the problems on your own.

Solved Examples on Profit %

1. Find Profit % if,
a) SP= 140 and CP= 100
b) SP= 220 and CP= 200
c) SP= 70 and CP= 50

Solution:

a) SP= 180 and CP= 140
Profit(P)= Selling price(SP) – Cost Price (CP).
= 180-140
= 40.
Profit = 40
Profit % = Profit/CP × 100.
= (40/100)×100
= 40%

b) SP= 220 and CP= 200
Profit(P)= Selling Price(SP) – Cost Price (CP).
= 220-200
= 20
Profit= 20
Profit% = profit/CP × 100.
= (20/200)×100
= (1/10)×100
= 10%.

c) SP= 60 and CP= 50
Profit(P)= Selling Price(SP) – Cost Price (CP).
= 60-50
= 10
Profit= 10
Profit%= profit/CP × 100.
= (10/50)×100
= (1/5)×100
= 20.

2. A man bought 50 bulbs for Rs 125 each. And sells them at Rs 150 each. Find the profit and profit percent?

Solution:

The selling price of the bulb= Rs 150
The cost price of the bulb= Rs 125.
So, Profit (P)= Selling Price(SP)- Cost Price(CP)
= Rs 150- Rs 125
= Rs 25
Profit = Rs 25.
Now to find the Profit percentage, apply the formula
Profit% = Profit/CP × 100.
= (25/125)×100
= (1/5)×100
= 20%.

Related Articles:

• Profit and Loss
• Calculate Loss and Loss Percent

Learn how to arrange Rational Numbers in Descending Order or Decreasing Order. In order to make you familiar with the concept of Rational Numbers in Decreasing Order we even listed examples explaining the step by step process. Check out the general method to arrange rational numbers from Largest to Smallest easily.

Procedure to arrange Rational Numbers from Largest to Smallest

Follow the easy guidelines on how to arrange Rational Numbers in Decreasing Order. They are as follows

Step 1: Express the given rational number in terms of the positive denominator.

Step 2: Find out the Least Common Denominator of the Positive Denominators.

Step 3: Express the given rational numbers using the LCM as Common Denominator.

Step 4: Compare the numerators and the one having the highest numerator is the largest one.

Solved Examples on Rational Numbers in Decreasing Order

1. Arrange the numbers 5/-3, 10/-7, -5/8 in Descending Order?

Solution:

Given Rational Numbers are 5/-3, 10/-7, -5/8

Express the Rational Numbers with Positive Denominators

5/-3 = 5*(-1)/-3*(-1) = -5/3

10/-7 = 10*(-1)/-7*(-1) = -10/7

-5/8 already has a positive denominator

Find the LCM of Positive Denominators

LCM of 3, 7, 8 is 168

Express the Rational Numbers with Common Denominator with the LCM obtained.

-5/3 = -5*56/3*56 = -280/ 168

-10/7 = -10*24/7*24 = -240/168

-5/8 = -5*21/8*21 = -105/168

Check the numerators of the rational numbers. Since all of them are negative numbers the lesser one is the highest fraction.

Therefore, Rational Numbers in Descending Order are -5/8, 10/-7, 5/-3.

2. Arrange the Rational Numbers 4/9, 5/6, 7/12 in Descending Order?

Solution: 

Given Rational Numbers are 4/9, 5/6, 7/12

Find the LCM of the Positive Denominators

LCM of 9, 6, 12 is 36

Express the Rational Numbers in terms of Common Denominator using the LCM obtained earlier.

4/9 = 4*4/9*4 = 16/36

5/6 = 5*6/6*6 = 30/36

7/12 = 7*3/12*3 = 21/36

Check the numerators of the rational numbers and the one having highest numerator is the highest rational number.

5/6, 7/12, 4/9 is the Descending Order of Rational Numbers.

3. Arrange the Rational Numbers 3/8, 5/7, 2/9 in Descending Order?

Solution:

Given Rational Numbers are 3/8, 5/7, 2/9

Determine the LCM of Positive Denominators.

LCM of 8, 7, 9 is 504.

Express the rational numbers with common denominator using the LCM obtained.

3/8 = 3*63/8*63 = 189/504

5/7 = 5*72/7*72 = 360/504

2/9 = 2*56/9*56 = 112/504

Check the numerators of the rational numbers and arrange the ones from highest to lowest.

Therefore Rational Numbers arranged in Descending Order is 5/7, 3/8, 2/9.

Let us learn in detail how to arrange Rational Numbers in Ascending Order. Have a look at the general method to arrange the Rational Numbers in Increasing Order. To help you get a better idea of the concept we even listed the solved examples provided step by step.

Procedure to arrange from Smallest to Largest Rational Numbers

Go through the below-listed guidelines in order to arrange Rational Numbers from smallest to largest. They are along the lines

Step 1: Express the given rational number in terms of a positive denominator.

Step 2: Determine the Least Common Multiple of the positive denominators obtained.

Step 3: Express each rational number with the LCM acquired as the common denominator.

Step 4: The number which has the smaller numerator is the smaller rational number.

Solved Examples for Rational Numbers in Ascending Order

1.  Write the following rational numbers in Ascending Order -3/5, -1/5, -2/5

Solution:

Since all the numbers have a common denominator the one with a smaller numerator is the smaller rational number. However, when it comes to negative numbers the higher one is the smaller one.

Therefore arranging the given rational numbers we get -3/5, -2/5, -1/5

2.  Arrange the rational numbers 1/2, -2/9, -4/3 in Ascending Order?

Solution:

Find the LCM of the denominators 2, 9, 3

LCM of 2, 9, 3 is 18

Express the given rational numbers with the LCM in terms of common denominator.

1/ 2= 1*9/2*9 = 9/18

-2/9 = -2*2/9*2 = -4/18

-4/3 = -4*6/3*6 = -24/18

Check the numerators of all the rational numbers expressed with a common denominator.

Since -24 is less than the other two we can arrange the given rational numbers in Ascending Order.

-4/3, -2/9, 1/2 is the Ascending Order of Given Rational Numbers.

3. Arrange the Rational Numbers 5/8, 4/-6, 3/5 in Ascending Order?

Solution:

Firstly, express the rational numbers with positive denominators by multiplying with -1

4/-6 = 4*(-1)/-6*(-1) = -4/6

So, find the LCM of the denominators 8, 6, 5

LCM of 8, 6, 5 is 120

5/8 = 5*15/8*15 = 75/120

-4/6 = -4*20/6*20 = -80/120

3/5 = 3*24/5*24 = 72/120

Check the numerator of the rational numbers having common denominators.

since -80 is the smallest that itself is the smallest rational number.

Therefore, 4/-6, 3/5, 5/8 are in Ascending Order.