What is the meaning of cost price in maths?

Every company and business works on the fundamental concept of profit and loss. It is very important to familiarize yourself with profit and loss, not only to run a business or com

What is the meaning of cost price in maths?

Every company and business works on the fundamental concept of profit and loss. It is very important to familiarize yourself with profit and loss, not only to run a business or company but also to keep an account of your own expenditure. Money is actually a tricky concept to explain to kids without giving them an opportunity to get hands-on experience. Parents often take their kids to the supermarket to make them learn about the price marked on every good and the calculation of total price. Later, kids come across the concept of discount on the cost price and the concept of comparing prices before purchasing. Comparing prices is also a form of profit and loss as you learn to save money by buying the same good at a comparatively lesser price.

The term 'Profit and Loss' is a concept developed from various applications to real-life problems which take place in our lives almost every day. When a good is re-purchased at a greater price then a profit is incurred. Similarly, if the good is repurchased at a lesser price then there is a loss.

We have come across the word profit and loss many times. Profit stands for gain, advantage or benefit whereas loss is the opposite of profit that involves expenditure as compared to gain.

Cost Price (CP): It is the amount at which a product is purchased. Sometimes it also includes overhead expenses, transportation cost, etc. For example, you bought a refrigerator at Rs 10,000 and spent Rs 2000 for transportation and Rs 500 for set up. So the total cost price is the sum of all the expenditure done, that is, Rs 12,500.

Selling Price (SP): It is the amount at which a product is sold. It may be more than, equal to or less than the cost price of the product. For example, if a shopkeeper bought a chair at Rs 500 and sold it at Rs 600, then the cost price of the chair is Rs 500 and the selling price of the chair is Rs 600.

Profit (P): If a product is sold at a price more than its cost price then the seller makes a profit. For example, a plot was purchased at Rs 50,000 and three years later it was sold at Rs 1,50,000 then there is a profit of 1 lakh.

Loss (L): If a product is sold at a price less than its cost price then the seller makes a loss.

For example, a phone is bought at Rs 20,000 and a year later it was sold for Rs 12,000 then the seller made a loss of Rs 8000.

Profit Percent (P%): It is the percentage of profit on the cost price.

Loss Percent (L%): It is the percentage of loss on the cost price.

Concept of Profit and Loss

Let us understand the concept in a simpler way by using profit and loss Math. Suppose a shopkeeper buys a pen at Rs 8 from the market and sells it at Rs 10 at his shop.

Amount invested by the shopkeeper or Cost Price = Rs 8

The amount received by the shopkeeper or Selling Price = Rs 10

Rule 1

If the cost is less than the Selling price then its a profit.

CP < SP ------ Profit

If the cost price is more than Selling Price then its a loss.

CP > SP ------ Loss

In the above example, the selling price is more than the cost price so that means the shopkeeper made a profit.

Rule 2

To find the amount of profit or loss, subtract the smaller value from greater value.

In the case of profit, the selling price is always more than the cost price.

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.

Here,

Cost Price = Rs 8

Selling Price = Rs 10

Profit = Selling Price - Cost Price

= Rs 10 - Rs 8

= Rs 2

Therefore, the shopkeeper made a profit of Rs 2 on selling a pen.

Now, let us find what percent of profit was made by the shopkeeper.

Rule 3:

In order to find the percentage, we divide the term we are finding the percentage of by total amount and then multiply the resultant with 100.

Profit % = \[\frac{{profit}}{{{\text{Cost Price}}}} \times \] 100

Loss % =\[\frac{{Loss}}{{{\text{Cost price}}}} \times \] 100

Here,

Profit % =\[\frac{{profit}}{{\operatorname{Cos} t{\text{ }}price}} \times 100\]

= \[\frac{2}{{10}} \times 100\]

= 20%

Thus, the shopkeeper made a profit of 20% of the cost price.

Summary of Profit and Loss Formula

Given below are profit and loss formulas and tricks to derive the value of other terms from the basic fundamental formulas:

Profit

Loss

CP < SP

Profit = Selling Price - Cost Price

Selling Price = Cost Price + Profit

Cost Price = Selling price - Profit

Profit % =\[\frac{{profit}}{{\operatorname{Cos} t{\text{ }}price}}\]\[ \times \]100

Cost Price =\[\frac{{profit}}{{profit{\text{ }}\% }}\]\[ \times \] 100

Profit = \[\frac{{profit}}{{100}} \times \] Cost Price

CP > SP

Loss = Cost Price - Selling Price

Cost Price = Selling Price + Loss

Selling Price = Cost Price - Loss

Loss % =\[\frac{{Loss}}{{{\text{Cost price}}}} \times \] 100

Loss = \[\frac{{Loss\% }}{{100}}\]\[ \times \] Cost Price

Cost Price = \[\frac{{Loss}}{{{\text{Loss }}\% }}\]\[ \times \] 100

Solved Examples:

Given below are the profit and loss examples found in real life:

  1. Find the Selling price of a bicycle of Rs 700 if
  2. Loss is Rs 50
  3. If Profit percentage is 50%

Solution:

Loss = Rs 50

Let SP be x.

We know in case of loss, the cost price is more than the selling price.

By using the formula of CP and SP.

Loss = CP - SP

Rs 50 = Rs 700 - x

x = Rs 700 - Rs 50

x = Rs 650

Thus, the selling price is Rs 650.

Profit % = 50

Let the profit be x.

Profit % = \[\frac{{profit}}{{\operatorname{Cos} t{\text{ }}price}}\]\[ \times \] 100

50 = \[\frac{x}{{700}} \times 100\]

\[50 = \frac{x}{7}\]

x = 7\[ \times \]50

x = Rs 350

Profit = Rs 350.

From the profit and loss Mathematics formula,

Profit = SP - CP

Rs 350 = SP - Rs 700

SP = Rs 700 + Rs 350

= Rs 1050

Thus, the selling price is Rs 1050 if the profit is 50% of the cost price.

2) A shopkeeper bought two TV sets at Rs 10,000 each such that he can sell one at a profit of 10% and the other at a loss of 10%. Find his overall profit or loss.

Solution:

The shopkeeper bought two TV sets. He made a profit by selling one and a loss by selling another. So let us divide the solution into two parts:

The cost price of TV = Rs 10,000

Profit % = 10 % of cost price

According to the formula,

Profit % = \[\frac{{profit}}{{\operatorname{Cos} t{\text{ }}price}} \times 100\]

\[10 = \frac{{profit}}{{10,000}} \times 100\]

\[10 = \frac{{profit}}{{100}}\]

Therefore, Profit = Rs 1000

If CP = Rs 10,000 and Profit = Rs 1000

Then, SP = 10,000+1000 = Rs 11000

The cost price of TV = Rs 10,000

Loss % = 10 % of cost price

According to the formula,

Loss % = \[\frac{{Loss}}{{\operatorname{Cos} t{\text{ }}price}} \times 100\]

\[10 = \frac{{Loss}}{{10,000}} \times 100\]

\[10 = \frac{{Loss}}{{100}}\]

Therefore, Loss = Rs 1000

If CP = Rs 10,000 and Loss = Rs 1000

Then, SP = 10,000-1000 = Rs 9000

Total Cost price = Rs 10,000 + Rs 10,000

= Rs 20,000

Total Selling price = Rs 11,000 + Rs 9000

= Rs 20,000

As the cost price is equal to the loss price, there is neither a profit nor a loss.

3) A shopkeeper bought 200 bulbs for Rs 10 each. Out of those, 5 bulbs were fused so he sold the remaining at Rs 12 each. Find the percentage of gain or loss.

Solution:

No of bulbs shopkeeper bought = 200

Cost of 1 bulb = Rs 10

Cost of 200 bulbs = Rs 10 x 200 = Rs 2000.

Therefore, the total cost price of 200 bulbs is Rs 2000

If 5 bulbs are thrown away then the number of bulbs left = 200 - 5 = 195.

Selling price of one bulb = Rs 12

Selling price of 195 bulbs = Rs 195 x 12 = Rs 2340

Therefore, the total selling price of 200 bulbs is Rs 2340

Selling price is more than the cost price, this means that the shopkeeper made a profit.

Profit = SP - CP

= Rs 340

Profit % =\[\frac{{profit}}{{\operatorname{Cos} t{\text{ }}price}} \times 100\]

= \[\frac{{340}}{{2000}} \times 100\]

= 17%

Thus, the shopkeeper made a profit of 17% on selling 195 bulbs at Rs 12.

4) Ankit bought a plot at Rs 2,25,000. He wanted an overall profit of 12% but he sold one-third of the plot at a loss of 8% so at what price should he sell the remaining plot of land?

Solution:

The cost price of the entire plot = Rs 2,25,000.

Cost price of 1/3rd of the plot = 1/3 \[ \times \] 2,25,000 = 75000

Loss % = \[\frac{{Loss}}{{\operatorname{Cos} t{\text{ }}price}}\]\[ \times \]100

\[8\% = \frac{{loss}}{{75000}}\]\[ \times \]100

loss = \[\frac{{8 \times 75000}}{{100}}\] = 6000.

Sumit suffered a loss of Rs 6000 on selling 1/3rd of the land

SP for 1/3rd of the land = 75000 - 6000 = 69,000.

To make a profit of 12% of 2,25,000, is

P%= \[\frac{p}{{cp}} \times 100\]

\[12 \times \frac{p}{{225000}} \times 100\]

\[\frac{{12 \times 225000}}{{100}}\]=P

Profit = Rs 27,000

Thus, to get a profit of Rs 27,000

SP= 2,25,000 + 27000 = Rs 2,52,000

Sumit has already sold 1/3rd of the land at Rs 69,000 thus he needs to sell the remaining land at Rs(2,52000-69000) i.e, Rs 1,83,000.

Therefore, Sumit needs to sell the remaining plot at Rs 1,83,000.

Percentage Vs Profit and Loss

Percentage, increase and decrease is closely related to profit, loss and their percentage in the profit and loss chapter. A percentage is a ratio that represents nothing but a fraction of 100. We use percentage for standardizing different quantities as the denominator is always 100. We not only represent data in percentage but also indicate the increase and decrease of value in percentage. The profit and loss concepts of increase percent relates to profit percent whereas decrease percent relates to loss percent. The only difference in profit and loss problems and percentage is that profit and loss percent deal with only money and play a great role in the financial calculation in all the businesses whereas increase and decrease percent can be used for anything.

Increase Percent

Suppose, the population of a village is 30,000. If the percentage of the population in the next two years is 50% of the actual population then what is the current population of the village?

We know that the actual or initial population of the village is 30,000. If 50% of the population is increased then that means 50% of 30,000 is increased.

50% of 30,000 =\[\frac{{50}}{{100}}\]of 30,000

= \[\frac{{50}}{{100}} \times 30,000\]

= 15,000

This means, in two years 15,000 people increased. So the current number of people is 30,000 + 15,000 which equals 45,000. Thus, the current population of the village is 45,000.

The relation between Increase Percent and Profit Percent.

Profit percent is the increased value of the cost price of the product. Suppose the initial value (Cost price) of a house was 6 lakhs after a few years the value of the house increased 50% of the initial value.

Increased value = Increase %=\[\frac{{increase}}{{Original{\text{ }}Value}} \times 100\]

= 50% of 6lakhs

= \[\frac{{50}}{{100}}\]of 6,00,000

= 3 lakhs

Current Value = 6 lakhs + 3 lakhs = 9 lakhs

If the house is sold at the current value then the selling price will be 9 lakhs.

According to profit and loss basics,

Profit = Selling Price - Cost Price

= 9 lakhs - 6 lakhs

= 3 lakhs

Note:

Increase %=\[\frac{{increase}}{{Original{\text{ }}Value}} \times 100\] whereas Profit %=\[\frac{{profit}}{{\operatorname{Cos} t{\text{ }}price}} \times 100\]

Therefore, profit is equal to the increase in the value and profit percentage is equal to the increased percentage.

The Difference between Increase Percent and Profit Percent.

Increase Percent

Profit Percent

It is calculated on the basis of the initial value

It is calculated on the basis of cost price

It is used to calculate the increase in the number of things, population, etc.

It is used to calculate the increase in the value of the commodity or product.

It may and may not deal with money.

It deals with money.

Learn about Profit and Loss with Vedantu

Mathematics is an art and it is the science and study of quality, structure, space, and change of any object. Mathematicians seek out patterns, formulate new conjectures, and establish the truth by rigorous deduction from appropriately chosen axioms and definitions.

It is the science of numbers, quantities, and shapes, how it is measured, and the relations between them. With knowledge of Mathematics, you can actually study the science that revolves around numbers, shapes, and patterns, how things can be counted, how particular things are organized. This subfield of Mathematics with alphabets is usually called algebra and there are lots more in Math.

Definition and Formula

Finding the amount of profit or loss is explained in detail in this chapter. If you subtract the smaller value from the greater value accordingly you can calculate the profit or loss percentage within minutes. In the case of profit, the selling price will always be more than the actual cost price. Profit = Selling Price - Cost Price. Similarly, in the case of loss, the cost price is more than the planned selling price.

The formula to calculate the profit percentage is

Profit % = Profit/Cost Price × 100.

The formula to calculate the loss percentage is

Loss % = Loss/Cost Price × 100.

To effectively calculate and produce a profit and loss statement at the end of a financial year, the total of a businesss revenue sources is added and that of the businesss total expenses that are connected to gaining revenue will be subtracted from the profit. The profit and loss statement, also called an income statement of any business, will provide details of a companys financial performance for any specific period of time. We would like to know the financial condition.

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