ICSE Class 6 Maths Chapter 10 Profit and Loss

Chapter 10: Profit And Loss

(Including Discount)

Basic Concept

If a man buys an article for ₹ 80 and sells it for ₹ 90, we say:

Cost price of the article = Price at which the article is bought = ₹ 80

Selling price of the article = Price at which the article is sold = ₹ 90

Since, the selling price of the article is more than its cost price, it is sold at a profit.

And Profit (gain) = ₹ 90 - ₹ 80 = ₹ 10

Thus, Profit (gain) = Selling Price - Cost Price i.e. Profit = S.P. - C.P.

S.P. is the short form of selling price and C.P. is the short form of cost price.

Similarly, if a man buys an article for ₹ 80 and sells it for ₹ 75,

The cost price of the article = ₹ 80

and its selling price = ₹ 75

Since the selling price is less than the cost price, the article is sold at a loss.

And Loss = ₹ 80 - ₹ 75 = ₹ 5

Thus, Loss = Cost Price - Selling Price, i.e. Loss = C.P. - S.P.

1. When the selling price is more than the cost price, a profit is made.

And, (i) Profit = Selling Price - Cost Price i.e. Profit = S.P. - C.P.

(ii) Selling Price = Cost Price + Profit i.e. S.P. = C.P. + Profit

(iii) Cost Price = Selling Price - Profit i.e. C.P. = S.P. - Profit

2. When the selling price is less than the cost price, a loss is made.

And, (i) Loss = Cost Price - Selling Price i.e. Loss = C.P. - S.P.

(ii) Selling Price = Cost Price - Loss i.e. S.P. = C.P. - Loss

(iii) Cost Price = Selling Price + Loss i.e. C.P. = S.P. + Loss

Teacher's Note

When you buy a toy for 100 rupees and sell it for 150 rupees, you have made a profit of 50 rupees - this basic transaction helps us understand how shopkeepers in your local market earn their living.

Exercise 10 (A)

1. A pen is bought for ₹ 12.40 and sold for ₹ 13.60. Find the profit made.

2. An article bought for ₹ 56 is sold at a gain of ₹ 8.50. Find its selling price.

3. Find the selling price of an article that is bought for ₹ 540 and sold at a loss of ₹ 68.50.

4. Find the cost price of a dressing table if, on selling it for ₹ 5,235, a profit (gain) of ₹ 847 is made.

5. On selling a sofa-set for ₹ 18,540; the manufacturer makes a loss of ₹ 1,935. How much did it cost to the manufacturer?

6. Pens bought at 5 for ₹ 60 are sold at 2 for ₹ 30. Find:

(i) the cost price of each pen.

(ii) the selling price of each pen.

(iii) the profit or loss made on selling one pen.

(iv) how much is gained or lost on selling 50 similar pens.

7. A man buys 300 articles at 4 for ₹ 6 and sold all of them at ₹ 2 each. Find:

(i) the cost price of one article

(ii) the profit made by the man on selling one article.

(iii) his total profit on selling all the 300 articles.

8. Ramesh sells pencils at 5 for ₹ 4. If he had bought 250 pencils at one rupee each, find:

(i) the selling price of each pencil.

(ii) the loss suffered on selling one pencil.

(iii) the total loss made on selling all the pencils.

9. A shopkeeper buys three articles for ₹ 375, ₹ 580 and ₹ 428 respectively. He is able to sell these articles for ₹ 436, ₹ 635 and ₹ 350 respectively. Find the gain or loss to the shopkeeper on the whole.

10. Rajesh buys an old sofa-set for ₹ 1,250 and spends ₹ 350 on its repairs.

(i) Find the total cost price of the sofa to Rajesh.

(ii) Find the profit or the loss made if Rajesh is able to sell the repaired sofa-set for ₹ 1,540.

11. An old scooter is brought for ₹ 7,800, and ₹ 1,850 is spent on its repairing, denting, painting, etc. Find: (i) the total cost price of the scooter.

(ii) if the repaired scooter is sold for ₹ 10,500, find the loss or the gain made.

Teacher's Note

When your parents buy vegetables from the market and later resell some homegrown produce, they calculate profit and loss to know if their effort was worthwhile.

Finding Profit Or Loss Percent

Profit% = (Profit / Cost Price) × 100% and Loss% = (Loss / Cost Price) × 100%

Both profit percent and loss percent are calculated on the cost price.

Example 1

Find the profit or loss percent when an old car, bought for ₹ 25,000, is sold for ₹ 28,000.

Solution

Given C.P. of car = ₹ 25,000 and, S.P. of it = ₹ 28,000

∴ Profit = ₹ 28,000 - ₹ 25,000 = ₹ 3,000

And Profit% = (Profit / C.P.) × 100% = (3000 / 25000) × 100% = 12%

Example 2

Peter bought an article for ₹ 400 and sold it for ₹ 380. Calculate his profit or loss as percent.

Solution

Since C.P. = ₹ 400 and S.P. = ₹ 380

∴ Loss = ₹ 400 - ₹ 380 = ₹ 20

And Loss percent = (Loss / C.P.) × 100% = (20 / 400) × 100% = 5%

Example 3

Mohan bought a T.V. set for ₹ 5,000 and sold it at a profit of 10%. Find the profit and the selling price of the T.V. set.

Solution

Since C.P. = ₹ 5,000 and Profit% = 10%

∴ Profit = 10% of ₹ 5,000 = (10 / 100) × ₹ 5,000 = ₹ 500

Also S.P. = C.P. + Profit = ₹ 5,000 + ₹ 500 = ₹ 5,500

Direct Method: S.P. = ((100 + P%) / 100) × C.P. = ((100 + 10) / 100) × ₹ 5,000 = ₹ 5,500

Example 4

A man bought an article for ₹ 450 and sold it at a loss of 20%. Find the loss and selling price of the article.

Solution

Since C.P. = ₹ 450 and Loss% = 20%

∴ Loss = 20% of ₹ 450 = (20 / 100) × ₹ 450 = ₹ 90

And S.P. = C.P. - Loss = ₹ 450 - ₹ 90 = ₹ 360

Direct Method: S.P. = ((100 - L%) / 100) × C.P. = ((100 - 20) / 100) × ₹ 450 = ₹ 360

Example 5

By selling a V.C.R. for ₹ 9,000, a profit of ₹ 1,000 is made. Find the profit percent.

Solution

Since S.P. = ₹ 9,000 and Profit = ₹ 1,000

∴ Cost Price = ₹ 9,000 - ₹ 1,000 = ₹ 8,000

And Profit% = (profit / C.P.) × 100% = (1000 / 8000) × 100% = 12.5%

Example 6

By selling a V.C.R. for ₹ 9,000, a loss of ₹ 1,000 is suffered. Find the loss percent.

Solution

Since S.P. = ₹ 9,000 and Loss = ₹ 1,000

∴ Cost Price = ₹ 9,000 + ₹ 1,000 = ₹ 10,000

And Loss% = (loss / C.P.) × 100% = (1,000 / 10,000) × 100% = 10%

Teacher's Note

When a shopkeeper announces a 20% profit on goods, they are using percent to show how much more money they earn compared to what they paid for the item.

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