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Constants and Variables are the popular terms used in algebra. Every expression or equation will be implemented with a combination of constants and variables. Constant is a fixed value in every expression and the variables are not fixed values. Learn different problems on Constants and Variables and get a grip on the complete concept.
Example:
x^2 + 2xy + 6 is an algebraic equation.
Here, 6 cannot be changed and it is the constant number in the equation, and x^2, 2xy values are varied depends on the values. So, x^2 and 2xy are variables in the equation.

Constant & Variables – Definitions

Constant: A Constant is defined as a fixed value in algebraic expressions or equations. Constant will not change with time and has a fixed value. For instance, Shoe Size will not vary at any point.

In an algebraic expression, x+y = 5, 5 is a constant value, and will not be changed.

Variables: Variables are terms that can change or differ over time. It will not have a fixed value unlike a constant. For example, the Height and Weight of a Person will not remain constant and will vary with time.

In an algebraic expression, x+y = 5, x and y are the variables and can be varied. Go through the below modules to know more about the key differences between Constants and Variables.

Difference Between Constants and Variables

See the main differences between Constants and Variables here. ?They are along the lines

• The main difference between the constants and variables, constant is a fixed value and a variable is not a fixed value.
• Constants are indicated by the numerical values and the variables are indicated by any alphabetical values like a, b, c, d, ………..z.

Examples of Constants and Variables

Find the Constants and Variables of Given Expressions.

1. x + y + 2 =0.

Solution:
The given expression is x + y + 2 = 0.
Here, x and y are variables.
2 is a constant number.

2. x^2 + y^2 + 20 = 0.

Solution:
The given expression is x^2 + y^2 + 20 = 0.
Here, x^2 and y^2 are variables.
20 is a constant number.

3. xy + x^2 + 15 = 0.

Solution:
The given expression is xy + x^2 + 15 = 0.
Here, xy and x^2 are variables.
15 is a constant number.

4. 2xy + 6 = x^2y.

Solution:
The given expression is 2xy + 6 = x^2y.
Here, 2xy and x^2y are variables.
6 is a constant number.

5. x^3 + y^3 = 2xy + 8.

Solution:
The given expression is x^3 + y^3 = 2xy + 8.
Here, x^3, y^3, and 2xy are variables.
8 is a constant number.

6. Find out the constants and variables in the below questions

(i) In 5m, 5 is a constant and m is a variable.
(ii) In -3ab, -3 is a constant and a and b are variables.
(iii) In 4b, 4 is constant and b is variable but together 4b is a variable.
(iv) If 2 is a constant and a is a variable, then 2 + a, 2 – a, 2/a, 2a, a/2, etc., are also variables.

FAQs on Constants and Variables

1. What is the main difference between variables and constant?
The major difference between variables and constants is variable is a varying quantity, and a constant is a fixed value.

2. What are the variables?
The variables are the terms in an algebraic equation that can be changed or that are not fixed. Example: a + b = 8, where a and b are the variables, and 8 is a constant.

3. What are constants? 
The constants are the value in an algebraic expression that cannot be modified or changed. For example, in an equation x + y = 9, 9 is the constant value.

4. What is an algebraic expression?
The algebraic expression is a combination of constants, variables, integers, and mathematical operations.

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PAGEIND Pivot Point Calculator

Calculate Profit and Profit Percent using Profit formula. Easily calculate the profit gained for a product by selling it. All the business or financial transactions are used the profit formula. The profit is calculated when the selling price of any product sold is greater than the cost price. Check out how the profit is calculated and know the profit gained by your business. We have included solved problems along with explanations.

Also, Read:

• Concept of Profit and Loss
• Practice Test on Profit and Loss
• Examples on Calculating Profit or Loss
• INFY Pivot Point Calculator

Formulas to Calculate Profit

If the selling price is more than the cost price (S.P. > C.P.), there is a profit. Various formulas to calculate profit are given below. Remember all of them for better learning.

• Formula for Profit Profit = S.P – C.P.
• Formula for Profit Percentage = Profit Percent Formula = (Profit x 100)/C.P.
• Gross Profit Formula = Gross Profit = Revenue – Cost of Goods Sold
• Profit Margin Formula = Profit Margin = (Total Income/Net Sales) x 100
• Gross Profit Margin Formula = Gross Profit Margin = (Gross Profit/Net Sales) x 100

Notation Used in Profit Formula

• S.P. = Selling Price i.e. the cost at which the product is sold
• C.P. = Cost price i.e. the cost at which the product is originally bought

Profit and Profit Percent Examples

Example 1.

Ram purchased 300 calculators at $100 each. He spent $5 on packing each calculator, paid $50 to the carrying for loading, and $500 on transportation. He sold 200 at a rate of $180 each and 100 at the rate of $80 each. Find his profit or loss percent in the whole transportation.

Solution:
Given that Ram purchased 300 calculators at $100 each.
C.P. of 1 calculator = $100
C.P. of 300 calculators = $100 x 300 = $30000
Money spent on packing 1 calculator = $5
Money spent on packing 300 calculators = $300 x 5 = $1500
Overhead expenses = $(1500 + 50 + 500) = $2050
C.P. of 300 calculators = Actual C.P. + Overhead expenses
C.P. of 300 calculators = $30000 + $2050 = $32050
S.P. of 300 calculators = S.P. of 200 calculators + S.P. of 100 calculators
S.P. of 1 calculator = $180
S.P. of 200 calculators = $180 x 200 = $36000
S.P. of 1 calculator = $80
S.P. of 100 calculators = $80 x 100 = $8000
S.P. of 300 calculators = $36000 + $8000 = $44000
S. P. > C. P., there is profit, therefore, profit – S.P. – C.P.
Profit = $44000 – $32050 = $11950
Profit% = P/C.P. x 100%
Profit% = $11950/$32050 x 100%
Profit% = 37.28%

The profit percentage is 37.28%.

Example 2.

A cloth merchant bought 25 shirts, each at a price of Rs 280. He sold each of them for Rs. 300. Find his percentage profit.

Solution:
Given that a cloth merchant bought 25 shirts, each at a price of Rs 280. He sold each of them for Rs. 300.
The profit percentage remains the same for one unit as well for all the units. Thus the calculations should be done for one unit only.
The Cost Price = Rs 280
Selling Price = Rs. 300
Profit = Selling Price – Cost Price
Substitute Selling Price and Cost Price in the above formula.
Profit = Rs. 300 – Rs 280 = Rs 20.
Now, find out the profit percentage formula.
Profit percentage = P/C.P. x 100%
Profit percentage = 100 × 20/280 = 7.14%

Therefore, the profit percentage is 7.14%

Example 3.

A retail fruit vendor buys pineapples at a score of Rs. 200/-,  and retails them at a dozen for Rs 156. Did he gain or lose in the transaction and what % was his gain or loss?

Solution:
Given that a retail fruit vendor buys pineapples at a score of Rs 200, and retails them at a dozen for Rs 156.
The cost price = Rs 220
C.P/Pineapple = 200/20 = 10
1 score = 20 nos
S.P = Rs.156/dozen
S.P/Pineapple = 156/12 = 13.
Profit = Rs. 13 – Rs. 10 = Rs. 3.
% Profit = 100 × 3/10 = 30%

Therefore, the profit percentage is 30%

FAQs on Profit and Profit Percent

1. How do I calculate profit percentage?

The profit percentage can be calculated using the below formula.
Formula for Profit Percentage = Profit Percent Formula = (Profit x 100)/C.P.

2. Is profit and profit percent different?

Yes, Profit is the difference between the Selling price and the Cost price when the Selling price is more than the Cost price.
P = SP – CP; SP>CP
Profit percent will obtain by dividing the Profit with Cost price and multiplying the resultant with the 100.
Profit percent = (Profit x 100)/C.P

3. What is the formula of Selling Price?

Selling Price can be found when the Profit Percentage and Cost Price are given is
SP = {(100 + P%)/100} x CP where SP is Selling Price, P% is Profit Percentage, and CP is Cost Price.

4. How to Calculate the Percentage Gain on an Investment?

• In calculating the percentage gain on an investment, first, determine the original cost.
• Next, Subtract the Cost Price from the Selling price of the investment.
• Take the gain from the investment and divide it by the original amount of the investment.
• Finally, multiply the result by 100 to get the percentage change in the investment.

Loss and Loss Percent is raised when the cost price is higher than the selling price. We can calculate the Cost Price when Sell Price and Loss Percent are given. Improve your preparation by referring to the complete article. Check out how to find the Cost Price and different solved examples on finding the Cost Price using Sell Price and Loss Percent from the below article. Also, find out the different formulas to use to find the cost price.

Also, See:

• Calculate Profit and Profit Percent
• Calculate Loss and Loss Percent
• IDFC Pivot Point Calculator

How to Calculate Cost Price using Sell Price and Loss Percent?

To find out the Cost Price using Sell Price and Loss Percent, use the below formula.
Cost price = selling price + loss
Cost price = selling price + loss% × cost price/100
The Cost price – loss% × cost price/100 = selling price
Cost price(1 – loss%)/100 = selling price
Cost price(100 – loss%)/100 = selling price
Also, Cost price = selling price × 100/100 – loss% (on cross multiplication)

Examples for finding Cost Price using Sell Price and Loss Percent

1. By selling a bicycle for $145, a shopkeeper loses 10%. How much percent would he gain or lose by selling it for $175?

Solution:
Given that by selling a bicycle for $145, a shopkeeper loses 10%.
The selling price = $145
Loss Percentage = 10%
We know that cost price = selling price × 100/100 – loss%
Substitute the selling price and the loss% in the above formula.
Cost price = $145 × 100/100-10
Cost price = $145 × 100/90
The Cost price = $14500/90
Cost price = $161.11
Therefore, cost price of the bicycle = $161.11
Now, if the selling price = $175, then gain = $175 – $161.11  = $13.89
Therefore, gain% = gain/cost price × 100
= 13.89/161.11 × 100
= 1500/150
= 8.62%

Therefore, he would have gained 8.62%.

2. If the selling price of a pen is $9 and the loss percent is 2%, then what is the cost price?

Solution:
Given that the selling price of a pen is $9 and the loss percent is 2%.
The selling price of a pen = $9
The loss percent is 2%.
Cost price = selling price × 100/100 – loss%
Substitute the selling price and the loss% in the above formula.
Cost price = $9 × 100/100 – 2
Cost price = $9 × 100/98
The Cost price = $900/98 = $9.18

Therefore, the cost price of the pen is $9.18.

3. Find out the cost price of the vehicle if the selling price is $3350 and the Loss is $154.

Solution:
Given that the selling price is $3350 and the Loss is $154.
The selling price of a pen = $3350
The loss = $154
Loss = Cost Price – Selling Price
Cost Price = Loss + Selling Price
Substitute the selling price and the loss in the above formula.
Cost Price = $154 + $3350
Cost Price = $3504

Therefore, the cost price of the vehicle is $3504.

FAQs on finding C.P using S.P and Loss%

1. What Does Cost Price Mean?

The cost price is the original price of an item. The cost is the total amount need to produce a product or carry out a service.

2. What is the Formula for the Cost Price?

The formula for Cost Price when the SP and L% are given
CP = {100/(100 – L%)} x SP where SP is the Selling Price and L is the Loss.

3. What are the types of Cost Prices?

Cost Price (CP) is the amount paid to buy the product is known as Cost Price. It is denoted by CP. Also, the cost price classified into two different categories. They are
Fixed Cost: The fixed cost is constant and it doesn’t vary under any circumstances.
Variable Cost: It could change depending on the number of units.

4. How to Calculate Cost Price?

Follow the below steps and find out the process to calculate cost price when the selling price and loss% are given.
1. Note down the selling price and loss%.
2. Write the formula of cost price i.e, CP = {100/(100 – L%)} x SP
3. Substitute the SP and L% in the above formula.
4. Calculate and find the Cost Price of the product.

Loss and Loss Percent are used for calculating the loss that occurred in a business. The loss is the difference between the cost price and the selling price. Loss Percent is the percent of loss in terms of actual cost price. The loss will occur when the selling price is less than the cost price. We have given how to Calculate Loss and Loss Percent and the formula of loss. Know the process to find them and learn how to apply them in your real life. Also, check the solved examples for a better understanding.

Do Read:

• Concept of Profit and Loss
• Calculate Profit and Profit Percent
• Examples on Calculating Profit or Loss
• EXIDEIND Pivot Point Calculator

Formula to Calculate Loss and Loss Percent

The loss occurs when a cost price is more than the selling price of a product in a business. The loss is calculated by subtracting the selling price from a cost price. The formula to calculate loss and loss percentage are

• Loss = Cost Price – Selling Price when the Cost Price is higher than the Selling Price.
  or
  Loss = C.P. – S.P. (C.P.>S.P.)
• Loss percentage = (Loss × 100) / C.P
• Selling Price: The Selling Price is the price of a product that was sold by the shopkeeper to the customer for a particular price. Selling price is denoted by S.P.
  Selling Price(SP)= Cost Price(CP) – Loss(L)
• Cost Price: The cost price is the price of a product it is the original cost of a product that was brought from the retailer. Cost Price is denoted by C.P.
  Cost Price(CP)= Selling Price(SP) + Loss(L)

Loss and Loss Percent Examples

Example 1.

A shirt was bought for $300 and sold for $250. Find the loss and loss percent.

Solution:
Given that a shirt was bought for $300 and sold for $250.
The cost price = $300
Also, the selling price = $250
Since, S. P. < C. P., there is loss.
Therefore, loss = cost price – selling price
Substitute the cost price and selling price in the above formula.
Loss = $300 – $250 = $50.
So, loss% = loss/cost price × 100%
Substitute the cost price and loss in the above formula.
loss% = $50/$300 × 100% = 16.66%

Therefore, the loss is $50 and the loss% is 16.66%

Example 2.

If the cost price of 30 pens is equal to the selling price of 35 pens, find a loss percent?

Solution:
Given that the cost price of 30 pens is equal to the selling price of 35 pens.
Let cost price of 1 pen = $1
Then cost price of 30 pens = $30
Also, cost price of 35 pens = $35
Since, selling price of 35 pens = cost price of 30 pens
Therefore, the selling price of 25 pens = $30
Therefore, loss = cost price – selling price
Loss = $35 – $30 = $5.
Therefore, loss% = loss/cost price × 100
loss% = $5/$35 × 100
loss% = 14.28%

Therefore, the loss is $5 and the loss% is 14.28%

Example 3.

Find the loss and loss percentage provided that the cost price is Rs. 60 and the selling price is Rs. 55.

Solution:
Given that the cost price is Rs. 60 and the selling price is Rs. 55.
The cost price = Rs. 60
Also, the selling price = Rs. 55
Since, S. P. < C. P., there is loss.
Therefore, loss = cost price – selling price
Substitute the cost price and selling price in the above formula.
Loss = Rs. 60 – Rs. 55 = Rs. 5.
So, loss% = loss/cost price × 100%
Substitute the cost price and loss in the above formula.
loss% = Rs. 5/Rs. 60 × 100% = 8.33%

Therefore, the loss is Rs. 5 and the loss% is 8.33%

Example 4.

If a house was bought by a man for Rupees 60 Lakhs and he sold it in 40 Lakhs. What is a loss percentage from this business?

Solution:
Given that a house was bought by a man for Rupees 60 Lakhs and he sold it in 40 Lakhs.
The cost price = Rs. 60 Lakhs
Also, the selling price = Rs. 40 Lakhs
Since, S. P. < C. P., there is loss.
Therefore, loss = cost price – selling price
Substitute the cost price and selling price in the above formula.
Loss = Rs. 60 Lakhs – Rs. 40 Lakhs = Rs. 20 Lakhs.
So, loss% = loss/cost price × 100%
Substitute the cost price and loss in the above formula.
loss% = Rs. 20 Lakhs/Rs. 60 Lakhs × 100% = 33.33%

Therefore, the loss is Rs. 20 Lakhs and the loss% is 33.33%

FAQs on Loss and Loss Percent

1. How do you calculate percentage loss?

Follow the below steps to find the percentage loss.
1. Note down the cost price.
2. Then, check out the Selling Price, and calculate the loss.
3. Substitute the Loss and cost price in the Loss percentage formula.
4. Finally, find the Loss percentage.
Loss percentage = (Loss × 100) / C.P

2. What are the Loss and Loss Percent Formulas?

The formula for Loss and Loss Percent are
Loss = C.P. – S.P. (C.P.>S.P.)
Loss percentage = (Loss × 100) / C.P where C.P. is cost price and S.P. is selling price.

3. What is the formula for S.P when Loss and C.P. are given?

The formula for Loss = C.P. – S.P.
Therefore, S.P. = C.P. – Loss

4. How to find the C.P. when Loss and S.P. are given?

The formula for Loss = C.P. – S.P.
Therefore, C.P. = Loss + S.P.

5. How to find loss from loss percentage?

The Loss percentage = (Loss × 100) / C.P
Firstly, multiply C.P with Loss percentage and then divide it by 100 to get a Loss from the loss percentage.
Loss = (Loss percentage × C.P)/100

Calculate Cost Price using Sell Price and Profit Percent when the inputs are Sell Price and Profit Percent and the output is Cost Price. By simply using the Cost Price formula, one can find out the Cost Price of a product. The cost price is always less than the selling price when the profit percent is given. We have detailed explanations and solved examples are included in this article. All the different methods to find Cost Prices using Sell Price and Profit Percent are given below.

Also, Check:

• Calculate Cost Price using Sell Price and Loss Percent
• Concept of Profit and Loss
• Calculate Profit and Profit Percent
• Calculate Loss and Loss Percent
• DABUR Pivot Point Calculator

How to Calculate Cost Price Using Sell Price and Profit Percent?

Follow the below process to find out the Cost Price Using Sell Price and Profit Percent. Also, get the Cost Price Formula to solve all the problems.

1. Write down the Sell Price and Profit Percent.
2. Note Down the Cost Price Formula.
3. Substitute the Sell Price and Profit Percent in the Cost Price Formula.
4. Finally, find out the Cost Price Using Sell Price and Profit Percent.

Cost Price Formula

Use the below formulas according to the problem and get the cost price easily.

Cost price = selling price – profit
Cost price = selling price – profit% × cost price/100
The Cost price + profit% × cost price/100 = selling price
Cost price(1 – profit%)/100 = selling price
Cost price(100 + profit%)/100 = selling price
Also, cost price = selling price × 100/100 + profit% (on cross multiplication);
Here, selling price and loss% is known.

Finding Cost Price Using Sell Price and Profit Percent Examples

1. A box was sold for $428 thereby gaining 8%. Find the cost price of the bag?

Solution:

Given that a box was sold for $428 thereby gaining 8%.
The selling price = $428
Gain Percentage = 8%
We know that cost price = selling price × 100/100 + gain%
Substitute the selling price and the gain% in the above formula.
Cost price = $428 × 100/(100 + 8)
Cost price = $428 × 100/108
The Cost price = $42800/108 = $396.29

Therefore, the cost price of the bag is $396.29

2. A fan was sold for $625 thereby gaining 15%. Find the cost price of the fan.

Solution:

Given that a fan was sold for $625 thereby gaining 15%.
The selling price = $625
Gain Percentage = 15%
We know that cost price = selling price × 100/100 + gain%
Substitute the selling price and the gain% in the above formula.
Cost price = $625 × 100/(100 + 15)
Cost price = $625 × 100/115
The Cost price = $62500/115= $543.47

Therefore, the cost price of the fan is $543.47

3. By selling a mobile for $1,240, a trader gains 10%. Find the cost price of the mobile?

Solution:

Given that by selling a mobile for $1,240, a trader gains 10%.
The selling price = $1,240
Gain Percentage = 10%
We know that cost price = selling price × 100/100 + gain%
Substitute the selling price and the gain% in the above formula.
Cost price = $1240 × 100/(100 + 10)
Cost price = $1240 × 100/110
The Cost price = $124000/110 = $1127.27

Therefore, the cost price of the mobile is $1127.27

The amount of a thing that can be sold is known as the Selling Price. It is denoted by SP. Also, the Selling Price is also called the sale price. The selling price can be calculated when the Cost price and Loss Percent are given. Solve all the given related to Selling price problems to get a complete grip on the concept. Also, check out the given explanation of problems to find the Selling Price using Cost and Loss Percent in the later modules.

Also, See:

• Calculate Cost Price using Sell Price and Loss Percent
• Calculate Cost Price using Sell Price and Profit Percent
• Calculate Profit and Profit Percent
• BANKNIFTY Pivot Point Calculator

How to Calculate Selling Price Using Cost and Loss Percent?

Follow the complete process to find out the Selling Price Using Cost and Loss Percent. Also, know the Cost Price Formula to solve all the problems easily.

1. Note down the Cost Price and Loss Percent.
2. Write Down the Selling Price Formula.
3. Substitute the Cost Price and Loss Percent in the Selling Price Formula.
4. Finally, find out the Selling Price Using Cost Price and Loss Percent.

Selling Price Formula when Cost and Loss Percent are Known

You can use the below formula to find the Selling Price of a product when you know the Cost and Loss Percent of that product. The formulas for Selling Price Formula when Cost and Loss Percent Known are

• Selling price = cost price – loss
• Selling price = cost price – loss% × cost price/100
• Selling price = 100 × cost price – loss% × cost price/100
• Selling price = (100 – loss%)cost price/100, [Here, cost price and loss% are known.]

Solved Examples to Find Selling Price using Cost and Loss Percent

1. Sam bought a dress for $250 and sold it to Olivia thereby suffering a loss of 10%. Find the selling price of the dress?

Solution:
Given that Sam bought a dress for $250 and sold it to Olivia thereby suffering a loss of 10%.
The cost price = $250
Loss Percentage = 10%
We know that selling price = (100 – loss%) cost price/100
Substitute the cost price and the loss% in the above formula.
Selling price = (100 – 10)250/100
Selling price = 90 × 250/100
The Selling price = $22500/100 = $225

Therefore, the Selling price of the dress is $225

2. Alex bought a laptop for $600 and sold it to Jack thereby suffering a loss of 12%. Find the selling price of the laptop?

Solution:
Given that Alex bought a laptop for $600 and sold it to Jack thereby suffering a loss of 12%.
The cost price = $600
Loss Percentage = 12%
We know that selling price = (100 – loss%) cost price/100
Substitute the cost price and the loss% in the above formula.
Selling price = (100 – 12)600/100
Selling price = 88 × 600/100
The Selling price = $52800/100 = $528

Therefore, the Selling price of the dress is $528

3. By selling a table for $630, Daisy loses 7%. At what price must she sell it to gain 10%.

Solution:
Given that By selling a table for $630, Daisy loses 7%.
Given that the selling price = $ 630
Loss % = 7%
We know, cost price = selling price × 100/100 – loss%
Substitute the selling price and the loss% in the above formula.
Therefore, cost price = 630 × 100/(100 – 7)
= 630 × 100/93
= $677.41
Now cost price = $677.41
Gain% = 10%
Therefore, selling price = (100 + gain%)cost price/100
= (100 + 10)677.41/100
= 110 × 6.77
= $744.7

At $744.7 price she can sell it to gain 10%.

The Selling Price is easily calculated when the Cost and Profit Percent are given. Calculate Selling Price using Cost and Profit Percent and apply them to your real-time problems. Check out the various problems and their solving methods to find the Selling Price when the Cost Price and Profit Percent are given. We have included real-life examples for your practice. Don’t miss any problems to learn the complete concept.

Also, See:

• Calculate Cost Price using Sell Price and Loss Percent
• Calculate Cost Price using Sell Price and Profit Percent
• Calculate Selling Price using Cost and Loss Percent

How to Calculate Selling Price Using Cost and Profit Percent?

Step by step procedure is given for you to find out the Selling Price Using Cost and Profit Percent. It is really easy to find the selling price when you know the cost price and Profit Percent. Therefore, check out the procedure and follow the steps while solving problems.

1. Find out the Cost price and Profit Percent from the given problem.
2. Note down the formula of Selling Price.
3. In the next step, substitute the Cost price and Profit Percent in the formula.
4. Finally, find the selling price.

Selling Price Formula when Cost and Profit Percent are Known

The Selling Price Formula is the important thing to remember to calculate all the problems when Cost and Profit Percent are given. Without missing, anyone, remember all the formulas and use them while calculating problems.

• Selling price = cost price + profit
• Selling price = cost price + profit%/100 × cost price
• The selling price = 100 × cost price + profit% × cost price/100
• selling price = (100 + profit%)cost price/100; [Here, cost price and profit% are known.]

Solved Examples to Find the Selling Price Using Cost and Profit Percent

1. Ram bought a Colors Box for $100 and sold it at a profit of 20%. Find the selling price of the book?

Solution:
Given that Ram bought a Colors Box for $100 and sold it at a profit of 20%.
The cost price of the Colors Box = $100
Profit Percentage = 20%
We know that selling price = (100 + profit%)cost price/100
Substitute the cost price and the profit% in the above formula.
Selling price = (100 + 20)100/100
Selling price = 120 × 100/100
The Selling price = $120

Therefore, the Selling price of the Colors Box is $120.

2. Alex bought a music system for $180. For how much should he sell the music system to gain 10%?

Solution:
Given that Alex bought a music system for $180.
The cost price of the music system = $180
Profit Percentage = 10%
We know that selling price = (100 + profit%)cost price/100
Substitute the cost price and the profit% in the above formula.
Selling price = (100 + 10)180/100
Selling price = 110 × 180/100
The Selling price = $198

Therefore, the Selling price of the music system is $198.

3. Robert bought a washing machine for $800 and sold it at a profit of 4%. Find the selling price of the washing machine?

Solution:
Given that Robert bought a washing machine for $800 and sold it at a profit of 4%.
The cost price of the washing machine = $800
Profit Percentage = 4%
We know that selling price = (100 + profit%)cost price/100
Substitute the cost price and the profit% in the above formula.
Selling price = (100 + 4)800/100
Selling price = 104 × 800/100
The Selling price = $832

Therefore, the Selling price of the washing machine is $832.

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MIDCPNIFTY Pivot Point Calculator

Discount is defined as the amount or percentage that deducted or reduced from the normal selling price of any product. Shortly, discount means the reduction in the price of a good or service. Refer to the marked price, list price and discount, and the formula of discount, and procedure to find out the discount, and solved examples in this article and get a grip on the total discount concept. Subtracting the Sale price from the Regular price minus gives the amount of discount. Check out various problems on discount and improve your math knowledge easily.

Discount Formula

Check out the formula of discount and Rate of Discount in the below section. Use the below formulas to find different problems on discount.

• Discount = List Price – Selling Price
• Therefore, Selling Price = List Price + Discount
• List Price = Selling Price + Discount

Discount Percentage Formula is

• Rate of Discount or Discount% = (Discount/List Price) * 100
• Selling Price = List Price ((100 – Discount)/100)%
• List Price = Selling Price (100/(100-Discount)%)

Concept of Discount

Sometimes, the retailers don’t directly sell the old items, defective items. They offer less price for those products to sell. Such a price is called the sale price. The difference between the Marked price (selling price) and the sale price is called a discount.
Discount = Marked Price – Sale Price

Marked Price

The price on the label of a product is called the Marked Price. The marked price is the price at which the product ready to be sold. Marked price is represented by MP.
Example: The price printed on the books is called the Marked Price.

List Price

The products that are manufactured in a factory and marked with a price by the retailer to sell them are called the List Price. The list price is represented as LP.

Selling price = Marked price – Discount
where the selling price is the amount that actually pays for the product when you purchase.
The marked price is the general price of the product without any discount.
Discount is a percentage of the Marked price.

Example:
If the cost of the pen is $10 and the shopkeeper reducing the amount of $8 on that pen, then there is a discount of $2 is available for that pen.
Sometimes, the discount is also available in percentages ‘%’.

Do Check Related Articles:

• Practice Test on Profit Loss and Discount
• Concept of Profit and Loss
• Calculate Profit and Profit Percent

How to Find Discount?

The below procedure will help you to find a discount on a product. Follow the procedure and practice different problems on discount using the below process.

1. The rate given for a product is considered as a percentage value.
2. In the next step, to find out the discount, multiply the rate by the original price.
3. To find the sale price, Subtract the discount from the original price.

Types of Discounts

Basically, Discounts are classified into three types. They are

Trade Discounts: The trade discounts are offered by the distributors. Trade discounts are the discounts where the amount of the product is reduced to sell the product.
Quantity Discounts: Quantity discounts are applied to a buyer depending on the number of items he purchased in greater numbers. Mainly, to sell the items in huge amounts to buyers, the sellers offer Quantity discounts.
Promotional Discounts: Promotional discounts are applied to do sales promotions. It is most preferable amongst shopkeepers. Generally, the Promotional discounts appear in % or buy 2 & get 1 free, etc.

Discount Examples

1. The marked price of a table fan is $ 750 and the shopkeeper offers a discount of 5% on it. Find the selling price of the table fan?

Solution:
Given that the marked price of a table fan is $ 750 and the shopkeeper offers a discount of 5% on it.
The Marked Price of the table fan = $750.
Discount on the table fan = 5%
We know that Discount = 5% of Marked Price
Discount = 5% of $ 750 = 750 * \(\frac { 5 }{ 100 } \) = 750 * 0.05 = 37.5
Discount = $37.5
To find the selling price of the table fan, subtract the discount from the Marked Price of the table fan.
Selling price = (Marked Price) – (discount)
Selling price = $750 – $37.5 = $712.5

Hence, the selling price of the table fan is $712.5.

2. A trader fixed the cost of his goods at 30% above the cost price and allows a discount of 15%. What is his gain percent?

Solution:
Given that a trader fixed the cost of his goods at 30% above the cost price and allows a discount of 15%.
Let the cost price be $ 100.
Therefore, the marked price = $130
We know that Discount = 15% of Marked Price
Discount = 15% of $130 = 130 * \(\frac { 15 }{ 100 } \) = 19.5
Discount =$19.5
To find the selling price of the table fan, subtract the discount from the Marked Price of the table fan.
Selling price = (Marked Price) – (discount)
Selling price = $130 – $19.5 = $110.5
Gain% = (Selling price – cost price)% = (110.5 – 100)% = 10.5%

Hence, the trader gains 10.5%.

3. A dealer purchased a cooler for $ 3830. He allows a discount of 6% on its marked price and still gains 5%. Find the marked price of the cooler?

Solution:
Given that a dealer purchased a cooler for $ 3830. He allows a discount of 6% on its marked price and still gains 5%.
The Cost price of the cooler = $ 3830
Gain% = 5%.
Now, find out the selling price.
To find the selling price, Substitute the Cost price and Gain% in the selling price formula.
Therefore, selling price = [{(100 + gain%)/100} × CP]
Selling price = $ [{(100 + 5)/100} × 3830] = $4021.5
The selling price is $4021.5
Let the marked price be $ x.
Then, the discount = 6% of marked price = 6% of $ x.
discount = $ {x × (6/100)} = = $ 3x/50
To find the selling price of the table fan, subtract the discount from the Marked Price of the table fan.
Selling price = (Marked Price) – (discount)
Selling price = $ x – $ 3x/50 = $47x/50
But, the SP = $4021.5
Therefore, $47x/50 = $4021.5
$47x = $4021.5 * 50
$47x = 201075
x = 201075/47 = $4278.19

Hence, the Marked price of the cooler is $4278.19.

4. How much percent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 15% on the marked price, he gains 30%?

Solution:
Let the cost price be $ 100.
Gain required = 30%.
Therefore, the selling price = $ 130.
Let the marked price be $x.
Then, discount = 15% of $x
discount = $ (x × 15/100)
discount = $ 3x/20
To find the selling price of the table fan, subtract the discount from the Marked Price of the table fan.
Therefore, selling price = (Marked Price) – (discount)
= $ {x – ($ 3x/20)
= $ 17x/20
Therefore, $ 17x/20 = 130
⇔ x = {130 × (20/17)} = 152.94
Therefore, marked price = $ 152.94.

Hence, the marked price is 52.94% above the cost price.

Successive Discounts

If two or more discounts are applied one after the other on a single product, then such discounts are called Successive Discounts. The Successive Discounts are also called discounts in series.

For example, if a discount of 30% is given for a product and later 10% of discount is given due to the reduced price. In such a situation, we can say successive discounts of 30% and 10% are given.

5. Find the single discount equivalent to two successive discounts of 30% and 20%.

Solution:
Let the marked price of the product be $ 100.
Then, the first discount on it = $ 30.
Price after first discount = $ (100 – 30) = $ 70.
Second discount on it = 20% of $ 70
= $ {70 × (20/100)} = $ 14.
Price after second discount = $ (70 – 14) = $ 56.
Net selling price = $ 56.

Single discount equivalent to given successive discounts = (100 – 56)% = 44%.

Fake Discounts

Fake Discounts also exist where the product pre-sale price may immoderately increase, or else the post-sale price of the product is actually its market price. This may feel the customers that they are getting a discount to make them purchase a product.

Frequently Asked Questions on Discounts

1. What is the Discount?

Discount is the amount deducted from the list price of the commodity before selling it to the customer.

2. How to Calculate Discount?

Check out the below steps to calculate the discount.
1. Find out the original price of the product.
2. Know the discount percentage.
3. Calculate the savings.
4. Calculate the sale price by subtracting the savings from the original price.
To calculate the discount, we need to subtract the selling price from the list price.
Discount = Selling Price – List Price

3. What is the Discounted Rate?

The discounted rate is also called the discount percentage. It is defined as the percentage by which list price is reduced before selling.

4. What is the Discount Percentage Formula?

The formula for Discount Percentage is
Rate of Discount or Discount% = (Discount/List Price) * 100
Selling Price = List Price ((100 – Discount)/100)%
List Price = Selling Price (100/(100-Discount)%)

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Are you a beginner to learn the concept of Skip Counting by 3S? If yes, then check out here to know each and every detail about this concept. Skip counting is considered a skill and also viewed as an arbitrary math skill. With the help of skip counting facts and definitions, you can improve learning the multiplication facts and along with the number sense. Skip counting deals with counting the numbers by 2S, 3S, 5S, etc Here in the below sections, we will see a detailed explanation on Skip Counting by 3S. Follow the facts, definitions, examples, etc.

Skip Counting by 3S – Introduction

Before, going to know how to skip count, first, we will learn about what is skip counting. Skip Counting is a technique or method of counting numbers other than 1. In the method of skip counting, we add the same numbers to the previous number each time.

Example:

Find the series of numbers with the skip count by 2?

Solution:

After applying the skip count by 2

we get the number series as 2,4,6,8,10,12…

Therefore, we get a series of even numbers.

Important Points of Skip Counting

• Skip Counting on any number is possible.
• This helps the numbers to count easily.
• The skip counting method involves a huge application in the multiplication of tables.
• Skip counting can be done with any numbers like 2S, 3S, 5S, 10S, 100S, etc.

Skip Counting by 3S – Important Points

• To skip count by number 3, keep adding the value 3 to get the next number.
• We can notice the diagonal patterns in the number grid when applying the skip counting by 3.
• Use the grid for the skip count and we miss out on two numbers and write the third digit.
• Skip counting by 3S from zero is essential in learning the 3’s timetable.
• For skip counting by 3S, we get the number line as 3,6,9,15,18,21,24,27,30 etc
• Learning the counting by 3 patterns till to 30 will help you with counting in 3’s with the larger numbers.

How to Skip Counting by 3?

Skip counting is the fastest way to count than simply counting one by one.

Skip counting by 3S means, adding the three numbers to get the next number, which means that we skip two numbers out in the process.

The number series of skip counting by 3S from zero, we have:

0,3,6,9,12,15,18,21,24,27,30

Since the pattern is not clear, the number grid will help you to understand the counting by three easily. With the help of the number grid, we can easily see the numbers that come next, and also we can see the numbers we skip while forming the number series.

To notice the pattern in the 3’s timetable, we have to look at the units digit column for the numbers.

Consider 30, we check for the units digit of 30 i.e., 0

Therefore, 0+3=3, hence, 30 + 3 = 33

Continuing to add three numbers, we get

30,33,36,39,42,45,48,51,54,57,60

Forward Skip Counting

In the forward skip counting, we count the numbers in the forward direction. It means that we skip the count of numbers for positive values. Counting the numbers with skip values has major applications in the real life. For suppose, if we want to count 100 marbles, use the skip counting method. If we count one-one marble, it consumes a lot of time. Thus, we use the skip count method, by any of the big numbers like 10 or 20, then we will count them quickly.

Backward Skip Counting

Backward skip counting is also essential for the students which implies counting to the negative numbers. For example, if we want to count by -2 then the number series is

-2,-4,-6,-8,-10 etc.

Strategies to Skip Counting

1. Questioning

A much-overlooked strategy of teaching is questioning. There are various questions that can give you clarity on the topic. To skip count by 2S, try asking the question like “In how many ways you can count to 24?” or you can also ask to “Can you count to 40 by 10’s? Why or Whynot?”

2. Use a Calculator

Generally, we don’t use calculators when solving skip counting problems. However, it can be a useful and fun tool when solving this skill. First of all, practice how to change the numbers by pressing the equal sign. This kind of strategy helps to build the number fluency and also to remember the skip counting values.

3. Play Game

This kind of strategy is used for kids. This is an easy process where kids can remember skip counting and also can have fun. Make the students stand or sit in a circle. Stand counting the student with a random number and then they continue to count by skipping the number until they go the complete way around the circle.

4. Use Manipulatives

To remember the method and rules easily, make use of manipulatives like paper clips, candy, snap cubes. With the help of these manipulatives, you can recite a string of numbers and can understand the purpose of skip counting.

Skip Counting by 2S

In this method, we add the number 2 for each counting. In this manner, we get alternate numbers. For example, if we start counting from 2, then by skipping the count of numbers, we get the number series as

2,4,6,8,10,12,14,16,18,20,22…

Skip Counting by 4

When we skip count by 4, then we have to add 4 in each step. The procedure we follow for skip count 4 is

0+4 = 4, 4+4 = 8, 8+4 = 12, 12+4=16, 16+4 = 20, 20+4 = 24,24+4 = 28 etc.

Skip Counting by 5

In this method, we add the number 5 for each counting. In this manner, we get numbers with a difference of 5. For example, if we start counting from 5, then by skipping the count of numbers, we get the number series as

5,10,15,20,25,30,35,40,45,50,55,60,65,70…

Skip Counting by 10

When we skip count by 10, then we have to add 10 in each step. The procedure we follow for skip count 10 is

0+10=10, 10+10=20, 20+10=30, 30+10=40, 40+10=50, 50+10=60…

Skip Counting by 25

In this method, we add the number 25 for each counting. In this manner, we get numbers with a difference of 25. For example, if we start counting from 25, then by skipping the count of numbers, we get the number series as

25,50,75,100,125,150,175,200,225… etc

Skip Counting by 100

In this method, we add the number 100 for each counting. In this manner, we get numbers with a difference of 100. For example, if we start counting from 100, then by skipping the count of numbers, we get the number series as

100,200,300,400,500,600,700… etc

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In this article, we are going to introduce a new concept that is Cube of the Sum of Two Binomials terms. We are providing the different problems with a clear explanation on this topic. Follow our page and get full of knowledge on it. Firstly, to find the cube of the sum of two binomials, we need to multiply the binomials term three times. Refer to Solved Examples on Cube of Sum of Two Binomials provided along with Solutions for better understanding of the concept.

How to find the Cube of Sum of Two Binomials?

For example, (x + y) ^3 = (x + y) (x + y)^2 is the example of a binomial expression.

Here, we have an equation in an algebra like (a + b)^2 = a^2 + 2ab + b^2.
By using the above equation, we can expand the cube term.
(x + y) (x + y)^2 = (x + y) (x^2 + 2xy + y^2).
Multiply the terms (x + y) and (x^2 + 2xy + y^2). Then we get
(x + y) (x^2 + 2xy + y^2) = x (x^2 + 2xy + y^2) + y (x^2 + 2xy + y^2).
= x^3 + 2x^2y + xy^2 + yx^2 + 2xy^2 + y^3.
= x^3 + 3x^2y + 3xy^2 + y^3.
= x^3 +y^3 + 3xy(x + y).

Also, Read: Cube of a Binomial

Cube of Sum of Two Binomials Examples

1. Determine the expansion of (x + 2y)^3.

Solution:
The given expression is (x + 2y)^3.
We have an equation on cubes like (x + y)^3 = x^3 + y^3 + 3xy(x + y).
By comparing the above expression with the (x + y)^3
Here, x = x and y = 2y
Substitute the terms in the equation (x + y)^3
That is, (x + 2y)^3 = x^3 + (2y)^3 + 3x(2y)(x + 2y).
= x^3 + 8y^3 + 6xy(x + 2y).
= x^3 + 8y^3 + 6x^2y + 12xy^2.

Therefore, (x + 2y)^3 is equal to x^3 + 8y^3 + 6x^2y + 12xy^2.

2. Evaluate (55)^3.

Solution:
The given one is (55)^3.
We can write it as (50 + 5)^3.
(x + y)^3 = x^3 + y^3 + 3xy(x + y).
By comparing the (50 + 5)^3 with the above expression.
x = 50 and y = 5.
Substitute the values in the expression.
(50 + 5)^3 = (50)^3 + (5)^3 + 3(50)(5)(50 + 5).
= 1,25,000 + 125 + 750(55).
= 1,25,000 + 125 + 41,250.
= 1,66,375.

Therefore, (55)^3 is equal to 1,66,375.

3. Find the value of 64x^3 + y^3 if 4x + y = 6 and xy = 5.

Solution:
The given expression is 64x^3 + y^3.
4x + y = 6.
Cube the terms on both sides. Then, we will get
(4x + y)^3 = (6)^3.
We have an equation (x + y)^3 = x^3 + y^3 + 3xy(x + y).
Here, x = 4x and y = y.
Substitute the values in the equation. Then,
(4x)^3 + y^3 + 3(4x)(y)(4x + y) = 216.
64x^3 + y^3 + 12xy(4x + y) = 216.
But 4x + y = 6 and xy = 5.
So, 64x^3 + y^3 + 12(5)(6) = 216.
64x^3 + y^3 + 360 = 216.
64x^3 + y^3 = -144.

Therefore, 64x^3 + y^3 is equal to -144.

4. If a + 1/a = 3, find the values of a^3 – 1/a^3.

Solution:
The given term is a + 1/a = 3
Cube the terms on both sides. Then, we will get
(a + 1/a)^3 = (3)^3.
We have an equation (x + y)^3 = x^3 + y^3 + 3xy(x + y).
By comparing the given terms with the equation.
Here, x = a and y = 1/a.
By substituting the terms in the given equation. We will get
(a + 1/a)^3 = a^3 + (1/a)^3 + 3a(1/a)(a + 1/a) = 27.
= a^3 + 1/a^3 +3(a + 1/a) = 27.
We have (a + 1/a) = 3. By substituting this value in the above expression.
a^3 + 1/a^3 + 3(a + 1/a) =27.
a^3 + 1/a^3 + 3(3) = 27.
a^3 + 1/a^3 +9 = 27.
a^3 + 1/a^3 = 27 – 9 = 18.

Therefore, a^3 + 1/a^3 is equal to 18.

5. Expand the term (2x + y)^3.

Solution:
The given expression is (2x + y)^3.
we have an equation (x + y)^3 = x^3 + y^3 + 3xy(x + y).
by comparing the (2x + y)^3 with the above equation.
Here, x = 2x and y = y.
(2x + y)^3 = (2x)^3 + (y)^3 +3(2x)(y)(2x + y).
= 8x^3 + y^3 + 6xy(2x + y).
= 8x^3 + y^3 + 12x^2y + 6xy^2.

The final answer is 8x^3 + y^3 + 12x^2y + 6xy^2.

A Rational Number is represented as a fraction. For example, x / y is a rational number. Here, the upper term of the fraction is called a numerator that is ‘x’, and the lower term of the fraction is called a denominator that is ‘y’. Both terms numerator (x) and denominator (y) must be integers. Integer numbers are both positive and negative numbers like -4, -3, -2, -1, 1, 2, 3, 4…etc… The most important thing in the rational numbers is the denominator of the rational number cannot be equal to zero.

Rational Numbers are 2/3, 4/5, 6/7, 8/9, 10/15, 20/4, 125/100, ….etc… Check out the complete concept of Rational Numbers in Terminating and Non-Terminating Decimals below.

Rational Numbers in Decimal Fractions

By simplifying the rational numbers, we will get the result in the form of decimal fractions. We have two types of decimal fractions. They are

• Terminating Numbers
• Non – Terminating Numbers

When we converted the rational numbers into a decimal fraction, we will get either finite numbers of digits or infinite numbers of digits after the decimal point. If we get the decimal fraction with the finite number of digits, then it is called Terminating Numbers. If we get the decimal fraction with the infinite number of digits after the decimal point, then it is called Non – Terminating Numbers.

Terminating Number

Example for Terminating Numbers are 1.25, 0.68, 1.234, 2.456, 3. 4567, 5.687, 6.24, 8. 46, ….etc….The below examples are in the form of rational numbers and we need to convert that numbers into the form of decimal numbers.
(1) x / y = 100 / 25 = 0.4
(2) x / y = 644 / 8 = 8.5
(3) x / y = 5 / 4 = 1.25

Non – Terminating Number

Example for Non – Terminating Numbers are 1.23333, 2.566666, 5.8678888, 3.467777, 4.6899999,…..etc… The below-mentioned x / y fraction indicates the rational numbers and by simplifying it, we will get the decimal numbers.
(1) x / y = 256 / 6 =42.66666…
(2) x / y = 10 / 3 = 3.33333…
(3) x / y = 20 / 9 = 2.222222…

Note: If a rational number (≠ integer) can be expressed in the form p/(2^n × 5^m) where p ∈ Z, n ∈ W, and m ∈ W then the rational number will become a terminating decimal. If not, the rational number becomes the Non – Terminating Numbers.

Examples of Repeating and Non-Repeating Decimals

1. Find out the conversion of rational numbers to terminating decimal fractions?

(i) 1/4 is a rational fraction of form p/q. When this rational fraction is converted to decimal it becomes 0.25, which is a terminating decimal fraction.

(ii) 1/8 is a rational fraction of form p/q. When this rational fraction is converted to decimal fraction it becomes 0.125, which is also an example of a terminating decimal fraction.

(iii) 4/40 is a rational fraction of form p/q. When this rational fraction is converted to decimal fraction it becomes 0.1, which is an example of a terminating decimal fraction.

2. Find out the conversion of rational numbers to nonterminating decimal fractions.

(i) 1/11 is a rational fraction of form p/q. When we convert this rational fraction into a decimal, it becomes 0.090909… which is a non-terminating decimal.

(ii) 1/13 is a rational fraction of form p/q. When we convert this rational fraction into a decimal, it becomes 0.0769230769230… which is a non-terminating decimal.

(iii) 2/3 is a rational fraction of form p/q. When this is converted to a decimal number it becomes 0.66666667… which is a non-terminating decimal fraction.

Irrational Numbers

You may see different types of numbers such as real numbers, whole numbers, rational numbers, etc. Now, let us check out the irrational numbers. Irrational numbers are also real numbers that are represented as a simple fraction. There is no repeating or no terminate pattern available in Irrational Numbers. the numbers which do not consist of exact square roots of integers treats as Irrational Numbers. Also, the Irrational Number is pi and that is equal to the value of 3.14.

Solved Problems on Rational and Irrational Numbers

Addition

Add the two rational numbers. For example x / y = 1 / 2 and p / q = 2 / 6
To add the two rational numbers, we need to find out the LCM of the denominators.
That is, LCM of 2 and 6 is 6.
x / y + p / q = 1 / 2 + 2 / 6 = (3 + 2) / 6 = 5 / 6.

Multiplication

Multiply the two rational numbers such as 2 / 3 and 5 / 6.
x / y = 2 / 3 and p / q = 5 / 6
x / y X p / q = 2 / 3 x 5 / 6
(xX p) / (y X q) = (2 x 5) / 3 x 6)
px / yq = 10 / 18 = 5 / 9.

Subtraction

Subtract the two rational numbers. Here, 5 / 8 and 12 / 5 are rational numbers.
x / y = 5 / 8 and p / q = 12 / 5
x / y – p / q = 5 / 8 – 12 / 5
For subtraction, we need to find out the LCM of denominator values.
LCM of 8 and 5 is 40.
5 / 8 – 12 / 5 = [(5 x 5) – (12 x 8)] / 40 = (25 – 96) / 40 = -71 / 40.

Division

To divide the two rational numbers, we need to cross multiply the terms. For example, x / y and p / q are two rational numbers.
(x / y) ÷( p / q) = (2 / 5) ÷ ( 3 / 7)
Cross Multiply the first fraction numerator with second fraction denominator and vice versa.
xq / py = (2 x 7) / (5 x 3 )
xq / py= 14 / 15.

Everyone must know the number of Months and Days in a year. One complete year has 365 days or 366 days. Here, a leap year contains 366 days which comes once every four years. One year whether it is a leap year or a normal year contains 12 months. Now, months are divided into days that is 28, 29, 30, or 31 days.

Every year starts with the month of January and ends with the month of December. In between these two months, we have February, March, April, May, June, July, August, September, October, and November. In the below table, you can see the number of months in a year, the name of the month, the number of days in every month, and the short-form of every month.

List of Months and Days

Below is the list of Months and Days in a year. Learn the number of months and days along with their short-form whenever you need them. They are along the lines

Months and Days Examples

Now, calculate the number of days in a year based on the number of days in every month. That is, Count starts from the month of January
= (31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31)
= 365 days for a common year.

Now, calculate the number of days for a leap year. That is,
= (31 + 29 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31)
= 366 days for a leap year.

Seven days are equal to 1 week. We need to divide the total number of days in a year by seven. That is,
365 / 7 = 52 weeks and 1 day.
And, for leap year
366 / 7 = 52 weeks and 2 days.
Every leap year is divided by four.

For example, 2000, 2004, 2008, 2012, 2016, 2020, 2024, and etc… are leap years. The remaining years, which are not divided by four are common years.

We have different seasons for every three months. That means December, January, and February comes under the winter season. March, April, and May considered as Spring Season. Next, the Summer season covers June, July, and August months. Finally, September, October, and November come under the autumn season. Totally four seasons in a year.