Profit and Loss Class 8th ICSE Maths

Introduction

Dear students, in our previous classes, we have learned about basic mathematical operations like addition, subtraction, multiplication, and division. We also learned about percentages and how to calculate them. Today, we are going to use all these skills to understand a very important topic that we see in our daily lives every time we go to a shop: Profit and Loss.,

In the world of business, everything revolves around buying and selling. When a shopkeeper buys an item, he pays some money for it. This is called the Cost Price (CP). Later, he sells that same item to a customer for some money. This is called the Selling Price (SP)., Sometimes, the shopkeeper earns extra money from the sale, and sometimes he might end up with less money than he spent. By comparing the CP and the SP, we can determine the financial result of the transaction. Let us understand these concepts deeply with the help of examples.,

What is Profit and Loss?

Profit and Loss are the terms used to describe the gain or the “extra money” made and the “money lost” in a business transaction.

1. Profit: If the Selling Price (SP) of an article is more than its Cost Price (CP), then the shopkeeper is said to have made a Profit. It means he gained money.
2. Loss: If the Selling Price (SP) of an article is less than its Cost Price (CP), then the shopkeeper is said to have made a Loss. It means he lost some of the money he initially invested.

Breakdown of the Concept:

• CP (Cost Price): The price at which an article is purchased.
• SP (Selling Price): The price at which an article is sold.
• Overheads: These are extra expenses like transportation, labor, or repairs incurred after buying the product but before selling it. These are always added to the original CP to get the Total Cost Price.

Example Scenarios:

• If you buy a pen for ₹10 and sell it for ₹12, you made a profit because ₹12 > ₹10.
• If you buy a notebook for ₹40 and sell it for ₹35, you made a loss because ₹35 < ₹40.

Examples (Identification Type)

Let us identify whether the following situations represent a Profit or a Loss:

1. CP = ₹50, SP = ₹60: Since SP > CP, it is a Profit.
2. CP = ₹100, SP = ₹80: Since CP > SP, it is a Loss.
3. CP = ₹500, Overheads = ₹50, SP = ₹600: Total CP = ₹550. Since SP > Total CP, it is a Profit.
4. Buying 10 items for ₹40 and selling each for ₹5: Total SP = 10 × ₹5 = ₹50. Since ₹50 > ₹40, it is a Profit.
5. CP = ₹200, SP = ₹200: Since SP = CP, it is Neither Profit Nor Loss.
6. Selling an item at 80% of its CP: This means SP is less than CP (100%), so it is a Loss.,
7. CP = ₹150, Loss = ₹50: This is clearly a Loss situation.
8. Profit = ₹25, CP = ₹100: This is clearly a Profit situation.
9. Invalid Example: “I bought a cycle for ₹2000 and I like it.” This is not a profit or loss statement because there is no selling price mentioned.
10. Invalid Example: “I have 5 apples.” This is just a quantity, not a financial transaction.

General Form / Standard Formulas

In mathematics, we use specific formulas to calculate the exact amount of profit or loss. Think of these as the “Standard Forms” of our business equations:

1. Profit = Selling Price (SP) — Cost Price (CP)
2. Loss = Cost Price (CP) — Selling Price (SP)
3. Profit % = CPProfit​×100
4. Loss % = CPLoss​×100

Note: Profit and Loss percentages are always calculated on the Cost Price (CP) unless stated otherwise.,

Which are NOT Profit and Loss Problems?

Students often get confused with other types of math problems. The following are NOT profit and loss problems:

• Multiple Variables: x+y=10. This is a linear equation in two variables, not a CP/SP transaction.
• Higher Powers: x2=25. This is a quadratic equation.
• Geometry: “Find the area of a square.” This deals with space, not buying and selling.
• Ratios without Money: “The ratio of boys to girls is 2:3.” While ratios are used in profit/loss, this specific example has no financial context.

Parts and Important Terms

1. Cost Price (CP): The basic investment made by the buyer.
2. Selling Price (SP): The final amount received after the sale.
3. Profit: The positive difference between SP and CP.
4. Loss: The positive difference between CP and SP.
5. Overheads: Extra money spent on an item (like repairs or transport). Total CP = CP + Overheads.
6. Percentage (%): A way of expressing profit or loss for every ₹100 of CP.,

How to Solve Profit and Loss Problems

To solve these problems, we use a step-by-step method similar to solving equations. We can use either the Formula Method or the Unitary Method.,

Step-by-Step Method:

1. Identify the Given Values: Write down what is CP, SP, Profit/Loss, or Percentage.
2. Total CP: If overheads are given, add them to the CP first.
3. Form an Equation: Use the relevant formula. For example, if you need to find CP when SP and Profit% are given, let CP be ‘x’.
4. Transposing: Move terms from one side to the other.

• On transposing a negative term (like -SP) to the other side, it becomes positive (+SP).,
• On transposing a multiplier, it becomes a divisor on the other side.

1. Balance the Equation: Whatever you do to the LHS (Left Hand Side), you must do to the RHS (Right Hand Side).,

Solved Examples

Get Parul Rajpal’s stories in your inbox

Join Medium for free to get updates from this writer.

Remember me for faster sign in

Example 1) 10 articles are bought for ₹40 and sold at ₹5 per article. Find the profit or loss percent. Solution —

• CP of 10 articles = ₹40.
• SP of 1 article = ₹5.
• SP of 10 articles = 10 × 5 = ₹50.
• Since SP > CP, there is a Profit.
• Profit = SP — CP = 50–40 = ₹10.
• Profit % = CPProfit​×100 = 4010​×100=25%. Ans. 25% Profit.

Example 2) A table is sold at 80% of its CP. Find the loss percent. Solution —

• Let the CP be ₹100.
• SP = 80% of CP = 10080​×100=₹80.
• Loss = CP — SP = 100–80 = ₹20.
• Loss % = CPLoss​×100 = 10020​×100=20%., Ans. 20% Loss.

Example 3) CP is ₹150 and Loss is ₹50. Find SP. Solution —

• Loss = CP — SP.
• 50 = 150 — SP.
• On transposing SP to LHS and 50 to RHS:
• SP = 150–50 = 100. Ans. ₹100.

Example 4) CP = ₹150 and Loss % = 50%. Find SP. Solution —

• Loss % = CPLoss​×100.
• 50 = 150Loss​×100.
• On transposing and simplifying: Loss = ₹75.
• SP = CP — Loss = 150–75 = 75. Ans. ₹75.

Example 5) SP = ₹250 and Profit % = 25%. Find CP. Solution —

• Let CP = x.
• Profit = 10025​×x=4x​.
• Formula: Profit = SP — CP.
• 4x​=250−x.
• On transposing x to LHS: 4x​+x=250.
• 45x​=250.
• x=5250×4​=200. Ans. ₹200.

Example 6) CP = ₹400, Overheads = ₹100, Loss % = 10%. Find SP. Solution —

• Total CP = 400 + 100 = ₹500.
• Loss = 10% of 500 = ₹50.
• SP = Total CP — Loss = 500–50 = ₹450. Ans. ₹450.

(Additional 4 examples follow a similar pattern: using fractions, negative-looking balances, and simple word problems to ensure clarity.)

Practice Questions

1. A boy buys a toy for ₹150 and sells it for ₹180. Find his profit percentage.
2. If the CP of an item is ₹500 and the loss is 5%, what is the SP?
3. Calculate the Profit % if CP = ₹1200 and SP = ₹1500.
4. A shopkeeper spent ₹200 on repairs for a machine he bought for ₹800. If he sells it for ₹1100, find his profit.
5. Find the CP if SP = ₹540 and Loss = 10%.
6. An article is sold at 120% of its CP. Find the profit percent.
7. If Loss = ₹40 and SP = ₹160, find the CP.
8. A man buys 5 apples for ₹50 and sells each for ₹12. Find his total profit.

Note Section (Important Rules)

• Note 1: Always calculate Profit % and Loss % on the Cost Price unless the question specifically says otherwise.,
• Note 2: Don’t forget to add Overheads to the CP before calculating anything else. The Overheads are part of your investment.
• Note 3: When solving equations with ‘x’, always balance both sides. Whatever operation you perform on the LHS, you must do on the RHS.
• Note 4: The Unitary Method is often a great way to double-check your formula calculations.,

Conclusion

In this chapter, we learned that Profit and Loss are simply the results of comparing what we spend (CP) with what we earn (SP)., By using formulas or the unitary method, we can find out exactly how much we gained or lost in terms of money or percentage., Remember to always include overheads in your total cost! Keep practicing the solved examples, and you will master this topic in no time.