Profit and loss Class 8th ICSE Maths / Selina Chapter 8

Introduction

Hello students! Have you ever wondered why a shopkeeper, a vegetable seller, or even a manager of a large company does business? Is it just to help us by providing products and services? While they do help us, the main intention behind any business is to earn profit. A business can only grow if it earns a profit; if it faces a loss, the business might eventually have to close down. Therefore, it is very important for everyone to understand the concept of Profit and Loss.

You might think that only businessmen need to know this topic, but that is not true! We use Profit and Loss in our daily lives all the time. For example, if you go shopping with your mother and buy an item worth ₹500 for only ₹400, you have saved ₹100, which is a form of benefit or profit for you. Similarly, if you buy a book from a bookstore for ₹80 and its original price was ₹100, you have experienced a gain. Any decision involving money involves the concept of Profit and Loss. In this chapter, we will learn how to calculate these values and understand how they affect our financial decisions.

What is Profit and Loss?

To understand Profit and Loss, we must first understand two very important terms: Cost Price (CP) and Selling Price (SP).

1. Cost Price (CP): This is the amount of money paid to buy an article. Because it is the price paid for buying, it is also called the Bying Price. Sometimes, buying an item involves extra costs like delivery charges or transportation; these are added to the buying price to find the actual Cost Price.
2. Selling Price (SP): This is the amount of money we receive after selling an article.

The Conditions for Profit and Loss:

• Profit (Gain): When the Selling Price (SP) is greater than the Cost Price (CP), we make a profit. This means more money came into your pocket than what went out.
• Loss: When the Cost Price (CP) is greater than the Selling Price (SP), we suffer a loss. This means you spent more to buy the item than what you received when you sold it.

Examples of Profit and Loss:

• Example 1: Buying a pen for ₹10 and selling it for ₹12. (Profit)
• Example 2: Buying a cycle for ₹3000 and selling it for ₹2500. (Loss)
• Example 3: Buying a mobile for ₹10,000 and selling it for ₹12,000. (Profit)
• Example 4: Buying a bat for ₹500 and selling it for ₹450. (Loss)

Examples (Identification Type)

Let us understand with the help of examples whether a transaction results in a Profit or a Loss.

1. CP = ₹50, SP = ₹60

• Result: Profit.
• Reason: Since SP (₹60) is greater than CP (₹50), it is a profit.

1. CP = ₹100, SP = ₹80

• Result: Loss.
• Reason: Since CP (₹100) is greater than SP (₹80), it is a loss.

1. Buying Price = ₹200, Delivery Charge = ₹20, SP = ₹250

• Result: Profit.
• Reason: Total CP = 200 + 20 = ₹220. Since SP (₹250) > Total CP (₹220), it is a profit.

1. CP = ₹500, SP = ₹500

• Result: No Profit, No Loss.
• Reason: Since CP and SP are equal, the balance is zero.

1. CP = ₹1200, SP = ₹1000

• Result: Loss.
• Reason: CP is greater than SP.

1. CP = ₹15, SP = ₹20

• Result: Profit.
• Reason: SP is greater than CP.

1. Buying Price = ₹40, Transport = ₹10, SP = ₹45

• Result: Loss.
• Reason: Total CP = ₹50. Since SP (₹45) is less than CP, it is a loss.

1. CP = ₹85, SP = ₹100

• Result: Profit.
• Reason: SP is greater than CP.

General Form / Standard Form

In mathematics, we use specific formulas to calculate the exact amount of profit or loss. These formulas are the “standard forms” for this chapter.

1. Formula for Profit: Profit=Selling Price (SP)−Cost Price (CP)
2. Formula for Loss: Loss=Cost Price (CP)−Selling Price (SP)
3. Formula for Profit Percentage: Profit %=(CPProfit​)×100
4. Formula for Loss Percentage: Loss %=(CPLoss​)×100

Important Note: Profit and Loss percentages are always calculated on the Cost Price (CP) because CP represents your initial investment.

Which are NOT Profit and Loss?

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It is important to know when these concepts do not apply or when a calculation is wrong:

1. Items not sold: If you buy a bag for ₹500 and keep it for yourself, there is no “Selling Price,” so there is no profit or loss.
2. Calculating % on SP: If you calculate profit percentage using the Selling Price in the denominator, your answer will be mathematically incorrect.
3. Ignoring Overheads: If you buy a machine for ₹1000 and pay ₹200 for repair, your CP is ₹1200, not ₹1000. Ignoring the ₹200 would give you a wrong CP.
4. CP = SP: As mentioned before, if the buying and selling prices are the same, there is no profit or loss.
5. Higher Powers: Unlike algebra where we have x2, in Profit and Loss, we deal with direct monetary values. Using squares of prices is not part of standard profit/loss calculations.

Parts and Important Terms

1. Cost Price (CP): The total money spent to acquire an item, including the buying price and extra expenses.
2. Selling Price (SP): The final money received after selling the item to someone else.
3. Overhead Expenses: Extra money spent on an item like transportation, labor, or packaging. These are always added to the buying price.
4. Profit: The extra money earned when you sell something for more than you paid.
5. Loss: The money you “lose” from your pocket when you sell something for less than you paid.
6. Profit/Loss Percentage: A way to compare two different businesses by seeing how much they earn or lose for every ₹100 invested.

How to Solve Profit and Loss Problems

Let us learn the step-by-step method to solve these problems. We will use the teaching phrases used in classrooms.

Step 1: Identify the values. Look for the Buying Price and any extra expenses. Step 2: Calculate Total CP. If there are overhead expenses, add them to the buying price. Step 3: Compare SP and CP.

• If SP>CP, it is a Profit.
• If CP>SP, it is a Loss. Step 4: Apply the Formula.
• On subtracting CP from SP, we get the Profit.
• On subtracting SP from CP, we get the Loss. Step 5: Calculate Percentage (if asked).
• On dividing the Profit/Loss by CP and multiplying by 100, we get the percentage.

Solved Examples

Example 1) A shopkeeper buys a toy for ₹100 and sells it for ₹150. Find the profit. Solution — CP = ₹100 SP = ₹150 Since SP>CP, it is a Profit. Profit=SP−CP Profit=150−100=50 Ans. ₹50

Example 2) Rahul bought a book for ₹100 and sold it for ₹80. Find the loss. Solution — CP = ₹100 SP = ₹80 Since CP>SP, it is a Loss. Loss=CP−SP Loss=100−80=20 Ans. ₹20

Example 3) A man buys a car for ₹100 and pays ₹40 for delivery. He sells it for ₹160. Find his profit. Solution — Buying Price = ₹100 Overhead Expenses (Delivery) = ₹40 Total CP = 100+40=₹140 SP = ₹160 Profit=SP−Total CP Profit=160−140=20 Ans. ₹20

Example 4) Calculate the profit percentage for Example 1 (CP = ₹100, Profit = ₹50). Solution — Profit %=(Profit/CP)×100 Profit %=(50/100)×100 On dividing and multiplying, we get 50%. Ans. 50%

Example 5) A shopkeeper buys an item for ₹10 and sells it for ₹12. Find the profit percentage. Solution — Profit=12−10=₹2 Profit %=(2/10)×100 On multiplying, 0.2×100=20%. Ans. 20%

Example 6) Shopkeeper A invests ₹1000 and earns ₹20 profit. Find the profit percentage. Solution — CP = ₹1000, Profit = ₹20 Profit %=(20/1000)×100 On simplifying the fraction, we get 2%. Ans. 2%

Example 7) A businessman buys petrol and pays for transportation. CP = ₹500, Transport = ₹50, SP = ₹600. Find Profit. Solution — Total CP = 500+50=₹550 SP = ₹600 Profit=600−550=50 Ans. ₹50

Example 8) If CP = ₹200 and Loss = ₹40, find SP. Solution — Loss=CP−SP On transposing SP to the other side, SP=CP−Loss SP=200−40=160 Ans. ₹160

Example 9) Find Loss % if CP = ₹50 and SP = ₹40. Solution — Loss=50−40=₹10 Loss %=(10/50)×100 Loss %=1/5×100=20% Ans. 20%

Example 10) Find Profit % if CP = ₹250 and SP = ₹300. Solution — Profit=300−250=₹50 Profit %=(50/250)×100 Profit %=1/5×100=20% Ans. 20%

Example 11) A wholesaler buys goods for ₹800 and spends ₹200 on packaging. He sells them for ₹900. Find Loss. Solution — Total CP = 800+200=₹1000 SP = ₹900 Since CP>SP, Loss=1000−900=100 Ans. ₹100

Example 12) In Example 11, find the Loss percentage. Solution — Loss %=(100/1000)×100 On dividing, we get 10%. Ans. 10%

Example 13) If SP = ₹120 and Profit = ₹20, find CP. Solution — Profit=SP−CP On transposing CP, CP=SP−Profit CP=120−20=100 Ans. ₹100

Example 14) A fruit seller buys apples for ₹400. 10% of apples are rotten. He sells the rest for ₹450. Find profit. Solution — CP = ₹400 SP = ₹450 Profit=450−400=50 Ans. ₹50

Example 15) Which is a better business: Earning ₹10 on ₹100 or ₹50 on ₹1000? Solution — Case 1: Profit % = (10/100)×100=10% Case 2: Profit % = (50/1000)×100=5% Ans. Case 1 is better because the profit percentage is higher.

Practice Questions

1. A boy buys a cycle for ₹1200 and sells it for ₹1500. Find the profit and profit percentage.
2. If CP = ₹80 and SP = ₹60, calculate the loss percentage.
3. A shopkeeper buys a TV for ₹10,000 and spends ₹500 on its transport. He sells it for ₹12,000. Find his total profit.
4. Find the SP if CP = ₹500 and profit is 10%.
5. Define Overhead Expenses with two examples.
6. If a man earns ₹20 profit on an investment of ₹200, find his profit percentage.
7. A table bought for ₹2500 is sold at a loss of ₹200. Find the selling price.
8. Why is profit percentage always calculated on CP?

Note Section

• Note 1: Always calculate Profit % and Loss % on the Cost Price (CP), never on the Selling Price.
• Note 2: Overhead expenses (like transport, labor, repairs) must always be added to the Buying Price to get the Total CP before starting any other calculation.
• Note 3: Profit and Loss percentages are useful for comparing different businesses, even if their investment amounts are different.
• Note 4: Ensure all values (CP and SP) are in the same unit (e.g., all in Rupees) before calculating.

Conclusion

In this chapter, we learned that profit and loss are essential parts of business and daily life. The most important thing to remember is the relationship between Cost Price and Selling Price. If you receive more than you spent, it is a Profit; otherwise, it is a Loss. Always remember to include overhead expenses in your CP and calculate your percentages based on that total investment. Happy calculating!