Introduction
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.
Terms related to Profit and 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
In the above example, the selling price is more than the cost price so that means the shopkeeper made a profit.
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.
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:
Solved Examples:
Given below are the profit and loss examples found in real life:
Find the Selling price of a bicycle of Rs 700 if
Loss is Rs 50
If Profit percentage is 50%
Solution:
CP = Rs 700
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.
CP = Rs 700
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:
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.
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.
Calculation
To effectively calculate and produce a profit and loss statement at the end of a financial year, the total of a business’s revenue sources is added and that of the business’s 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 company’s financial performance for any specific period of time. We would like to know the financial condition.
FAQs on Profit and Loss
Maintain a separate revision note for writing down the formulas, theories, and methods followed throughout the chapter to get hold of what is actually happening. Try to find solutions yourself then self-evaluate so that you will know where you make mistakes and which part needs extra attention. Understand the complete syllabus and be ready with the appropriate guidance and solutions. Determine the areas of improvement and work on them to score better. Keep the exam paper neat and presentable. Answer in steps so you can actually fetch step marks even if you get the answers wrong.
2. How are profit and loss calculations used in our daily life?
Calculating time and cost for travel is also a form of profit and loss because you will have to calculate how much fuel will cost you to travel a certain distance and what comes under your budget. Understanding the concept of how the loans for cars, trucks, homes, schooling or other purposes work also requires deep knowledge of how EMI are calculated and how much you need to invest. In business and working in any organization also requires calculations. Life is always a calculation and race between profit and loss.
3. How do profit and loss calculations help in shaping your career?
Graduates who have knowledge in calculating the profit and loss are able to demonstrate well using their strong analytical and problem-solving skills and handle the situation better. The jobs available to these graduates are very much diverse and highly paid. You could pursue careers in areas such as insurance, economics, research, IT and get into more secured and reliable jobs in the market. It can help you score full marks and boost up your percentage hence there are high chances to get placed in the most reputed organization with a good salary structure.
This is a common problem every student will face before their examinations. They need to select a place where they might feel comfortable and peaceful to sit and study for hours. Usually, a silent place will help you store many things in your memory better and longer and will help you do the calculations perfectly. Try writing down the concepts, formulas and theories separately in a notebook and revise them whenever you get the time and even before entering the exam hall.
The Vedantu website provides lots of solved past years' question papers and some sample question papers for students to help them prepare well. Try working out as many question papers as possible instead of just reading out formulas because Math is a subject you will actually need to solve. By practicing in this way you will get a hold of time management by analyzing how much time you can actually spend on 1 mark or 5 mark questions instead of wasting time in the beginning and leaving behind important higher scoring questions.
