🎯 Create Your Practice Worksheet
You must start a new test before attempting answers. Answers stay hidden until you check each question.
Your questions will appear here
Choose your settings and press Start New Test.
📚 Class 9 Profit and Loss — Complete Practice Guide
Profit and loss is one of the most useful applications of percentages in school mathematics. It connects arithmetic with everyday situations such as buying and selling goods, comparing prices, calculating discounts and understanding how much money is gained or lost in a transaction. This DigiSadhan online worksheet is designed to help Class 9 students practise these ideas step by step. You can select the number of questions, choose a question type, select a difficulty level and optionally start a timed test.
1. Cost Price and Selling Price
Cost Price (CP) is the amount paid to buy an article. Selling Price (SP) is the amount received when that article is sold. These two values are the foundation of profit and loss questions. If SP is greater than CP, there is a profit. If SP is less than CP, there is a loss. Always identify CP and SP before choosing a formula.
Loss = CP − SP
2. Profit Percentage
Profit percentage tells us how large the profit is compared with the original cost. The percentage is calculated using the cost price as the base. For example, if an article costs ₹500 and is sold for ₹600, the profit is ₹100. Therefore the profit percentage is 100/500 × 100 = 20%.
3. Loss Percentage
When an article is sold for less than its cost price, the seller makes a loss. The loss percentage is measured against the cost price, not the selling price. This distinction is important because using the wrong denominator produces an incorrect answer.
4. Finding Selling Price
When the cost price and required profit percentage are known, the selling price can be found directly. A profit of p% means the selling price is 100 + p percent of the cost price.
For a loss of l%, the selling price is 100 − l percent of the cost price.
5. Finding Cost Price
Reverse questions ask you to find CP when SP and the percentage are given. For a profit of p%, divide the selling price by (100 + p) and multiply by 100. For a loss of l%, divide the selling price by (100 − l) and multiply by 100.
CP = SP × 100 ÷ (100 − Loss%)
6. Marked Price and Discount
The marked price (MP) is the price written on an article before a discount is applied. A discount reduces the marked price to obtain the selling price. Students should not confuse discount percentage with profit percentage. Discount is calculated on MP, while profit or loss percentage is normally calculated on CP.
Discount% = (Discount ÷ MP) × 100
SP after discount = MP × (100 − Discount%) ÷ 100
7. Successive Changes
When a price is changed more than once, percentages should not simply be added in every situation. For example, a 10% increase followed by a 10% decrease does not return the original value. Apply the first percentage to the starting value, then apply the second percentage to the new value. This worksheet includes successive-change questions to strengthen this skill.
8. How to Solve Word Problems
Read the question carefully and list the known quantities. Label CP, SP, MP, discount, profit or loss before calculating. Decide which formula matches the information. Keep the units consistent and perform a quick reasonableness check. If an item is sold at a profit, the final SP should be greater than CP. If it is sold at a loss, SP should be lower than CP.
9. Smart Practice Strategy
Start with Easy questions to build speed. Move to Medium questions when the basic formulas are comfortable, and use Hard questions for exam preparation. Try a timed test without looking at answers. After checking, use the Show Answer button only when needed. The progress bar and score panel help students see how much of the worksheet has been completed.
10. Key Formula Revision
Loss = CP − SP
Profit% = Profit/CP × 100
Loss% = Loss/CP × 100
SP = CP(100 + profit%)/100
SP = CP(100 − loss%)/100
Discount = MP − SP
Discount% = Discount/MP × 100
Regular practice is more effective than memorising formulas once. Use this free DigiSadhan Class 9 Profit and Loss worksheet repeatedly with different question counts, types and difficulty levels. Because the worksheet is generated dynamically, the questions can be shuffled for a fresh practice session. The layout is responsive, so students can practise comfortably on phones, tablets or computers.