Profit and Loss Class 6 ICSE — Chapter 10
Profit and loss class 6 ICSE is the chapter where you learn to measure what you gain or lose when you sell an article. Every purchase has a cost price (C.P.), the amount you pay to buy it. Every sale has a selling price (S.P.), the amount you receive. This chapter compares the two, finds profit or loss, expresses it as a percent, and then handles overheads and discount.
Download Profit and Loss Class 6 ICSE Mathematics Chapter 10 PDF
Download the Profit and Loss Class 6 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 8 pages, 5 sections, 41 questions.
What is inside Chapter 10
8 pages · 5 sections · 24 worked examples · 41 exercise questions
| Section | Title |
|---|---|
| 10.1 | BASIC CONCEPT |
| 10.2 | Finding Profit or Loss Percent |
| 10.3 | To find C.P. when S.P. and profit percent or loss percent are given |
| 10.4 | OVERHEADS |
| 10.5 | DISCOUNT |
- EXERCISE 10 (A): 11 questions
- EXERCISE 10 (B): 11 questions
- EXERCISE 10 (C): 19 questions
10.1 BASIC CONCEPT
Cost price is the price at which you buy an article. Selling price is the price at which you sell it. When the selling price exceeds the cost price, you make a profit. When it falls short, you make a loss.
Six relations connect the two prices. They appear throughout the exercises, so it helps to learn them as a set:
- \text{Profit} = \text{S.P.} - \text{C.P.}
- \text{S.P.} = \text{C.P.} + \text{Profit}
- \text{C.P.} = \text{S.P.} - \text{Profit}
- \text{Loss} = \text{C.P.} - \text{S.P.}
- \text{S.P.} = \text{C.P.} - \text{Loss}
- \text{C.P.} = \text{S.P.} + \text{Loss}
The logic is simple. Profit adds to what you paid, so selling price equals cost price plus profit. Loss takes away from what you paid, so selling price equals cost price minus loss. Reverse any relation to find the missing term.
Try this pattern. An article is bought for ₹120 and sold for ₹150. Since ₹150 is greater than ₹120, there is a profit. The profit is \text{₹ }150 - \text{₹ }120 = \text{₹ }30.
10.2 Finding Profit or Loss Percent
Percent makes profit comparable across different price levels. A ₹5 profit on a ₹10 article is very different from a ₹5 profit on a ₹500 article. Percent standardises the comparison.
Both percent formulas use the cost price as the base. This is the rule you must remember across the Class 6 ICSE syllabus. The percentage work you did in the earlier chapter on percentage builds directly into these formulas.
\text{Profit}\% = \frac{\text{Profit}}{\text{C.P.}} \times 100\% \quad \text{and} \quad \text{Loss}\% = \frac{\text{Loss}}{\text{C.P.}} \times 100\%
Why cost price? The cost price is what you actually invested. Percent is measured on the money you put in, not the money you took out. That is the convention every shop follows.
There is also a direct method to find the selling price. Add the profit percent to 100, or subtract the loss percent from 100. Then take that fraction of the cost price.
\text{S.P.} = \frac{100 + P\%}{100} \times \text{C.P.} \quad \text{or} \quad \text{S.P.} = \frac{100 - L\%}{100} \times \text{C.P.}
Here is the direct method in action. An item is bought for ₹2,000 and sold at a 15% profit. First find the profit: \frac{15}{100} \times 2000 = 300. Then add it to the cost price: 2000 + 300 = 2300. The direct formula gives the same result: \frac{100 + 15}{100} \times 2000 = 2300. So the selling price is ₹2,300.
A common mistake is using the selling price as the percent base. That produces a different, wrong answer. Always use the cost price.
10.3 To find C.P. when S.P. and profit percent or loss percent are given
Sometimes you know the selling price and the percent, but not the cost price. The reverse formulas recover it directly from the selling price.
\text{C.P.} = \frac{100}{100 + \text{profit}\%} \times \text{S.P.} \quad \text{when profit percent is given}
\text{C.P.} = \frac{100}{100 - \text{loss}\%} \times \text{S.P.} \quad \text{when loss percent is given}
The denominator shows what the percent does to 100. Profit percent makes the denominator larger, so the cost price comes out smaller than the selling price. Loss percent makes the denominator smaller, so the cost price comes out larger. That makes sense: a loss means you paid more than you received.
Here is the pattern. An article is sold for ₹1,200 at a 20% profit.
\text{C.P.} = \frac{100}{100 + 20} \times 1,200 = \frac{100}{120} \times 1,200 = 1,000
So the cost price was ₹1,000. Check it: 20% of ₹1,000 is ₹200, and ₹1,000 + ₹200 = ₹1,200, which matches the selling price.
10.4 OVERHEADS
Buying goods usually costs more than the purchase price alone. You may spend on transport, travelling, or repairs. These extra expenses are called overheads.
Overheads are added to the purchase price. The total becomes the true cost price. Profit or loss percent is then calculated on this total cost price, not the purchase price alone.
The reason is simple. You spent that extra money to get the goods ready for sale. If you ignore it, your profit looks bigger than it really is.
Here is the pattern. Goods are bought for ₹900 and ₹150 is spent on transport. The total cost price is ₹900 + ₹150 = ₹1,050. The goods are sold for ₹1,200. Profit = ₹1,200 − ₹1,050 = ₹150.
A frequent error is forgetting the overheads and working with the purchase price alone. That inflates the profit and gives a wrong percent.
10.5 DISCOUNT
Most articles carry a price printed on them or on a label. That printed price is the marked price (M.P.). To clear surplus stock or boost sales, shopkeepers reduce this price by a certain percent. The reduction is the discount.
Three rules govern discount. First, discount is always calculated on the marked price. Second, sale price equals marked price minus discount. Third, discount percent is the discount divided by the marked price, times 100.
\text{Sale Price} = \text{Marked Price} - \text{Discount}
\text{Discount}\% = \frac{\text{Discount}}{\text{Marked Price}} \times 100\%
The marked price is the announced reference price, so the reduction is measured against it. This keeps the discount percent consistent no matter how the shopkeeper sets the marked price.
Here is the pattern. A jacket is marked at ₹2,500 and sold at a 10% discount. Discount = 10% of ₹2,500 = ₹250. Sale price = ₹2,500 − ₹250 = ₹2,250. This chapter is one of several in the Class 6 Mathematics book.
What to practise from Profit and Loss Class 6 ICSE
Three exercise blocks test the skills in this ICSE chapter. Each builds on the one before it.
- EXERCISE 10 (A) — 11 questions on the basic relations between C.P., S.P., profit, and loss.
- EXERCISE 10 (B) — 11 questions on profit and loss percent, including the direct method for finding S.P.
- EXERCISE 10 (C) — 19 questions mixing overheads, discount, and reverse problems for C.P.
Here is the complete set of formulas from this chapter in one place.
| Situation | Formula |
|---|---|
| Profit | \text{Profit} = \text{S.P.} - \text{C.P.} |
| Loss | \text{Loss} = \text{C.P.} - \text{S.P.} |
| S.P. with profit | \text{S.P.} = \text{C.P.} + \text{Profit} |
| S.P. with loss | \text{S.P.} = \text{C.P.} - \text{Loss} |
| Profit percent | \text{Profit}\% = \frac{\text{Profit}}{\text{C.P.}} \times 100\% |
| Loss percent | \text{Loss}\% = \frac{\text{Loss}}{\text{C.P.}} \times 100\% |
| S.P. from profit percent | \text{S.P.} = \frac{100 + P\%}{100} \times \text{C.P.} |
| S.P. from loss percent | \text{S.P.} = \frac{100 - L\%}{100} \times \text{C.P.} |
| C.P. from profit percent | \text{C.P.} = \frac{100}{100 + P\%} \times \text{S.P.} |
| C.P. from loss percent | \text{C.P.} = \frac{100}{100 - L\%} \times \text{S.P.} |
| Sale price | \text{Sale Price} = \text{M.P.} - \text{Discount} |
| Discount percent | \text{Discount}\% = \frac{\text{Discount}}{\text{M.P.}} \times 100\% |
Watch for these three traps when you practise.
- Calculating profit or loss percent on the selling price instead of the cost price.
- Forgetting to add overheads to the purchase price before computing percent.
- Applying the discount to the selling price instead of the marked price.
Each exercise maps to a question type. Exercise 10 (A) tests the six basic relations. Exercise 10 (B) tests percent problems and the direct method. Exercise 10 (C) combines overheads, discount, and reverse C.P. problems. You can confirm the full syllabus on the official CISCE board website.
Profit and Loss Class 6 ICSE frequently asked questions
What is the profit and loss formula for class 6 ICSE?
Profit = S.P. − C.P. when the selling price exceeds the cost price. Loss = C.P. − S.P. when it falls short. Every other formula in this chapter is a rearrangement of these two.
In Class 6 ICSE profit and loss, is percent based on cost price or selling price?
Always on the cost price. Both Profit% and Loss% use C.P. as the base. Using S.P. gives a wrong answer.
What is an overhead in this Class 6 ICSE chapter?
Overheads are extra expenses such as transport, travelling, or repairs. They are added to the purchase price to get the total C.P. Profit or loss percent is then calculated on the total.
What is the difference between marked price and selling price in Class 6 ICSE?
Marked price is the printed price on the article. Selling price is what the customer actually pays after the discount. Sale Price = Marked Price − Discount.
How do I find cost price in this profit and loss ICSE chapter when selling price and profit percent are given?
Use C.P. = 100/(100 + profit%) × S.P. When the loss percent is given, use C.P. = 100/(100 − loss%) × S.P.
Reference: ICSE Class 6 Mathematics textbook material, chapter 10: Profit and Loss — CISCE-aligned.