MathematicsStd: VI

A shopkeeper buys goods at a price and then sells them to us usually at a higher price.

The price at which a shopkeeper sells the goods to his customer is the selling price (S.P.).

The price which a shopkeeper pays to buy the goods is the cost price (C.P.).

(Contd…)

If the shopkeeper sells the goods at a price higher than the cost price he makes a gain or profit.

If the shopkeeper sells the goods at a price lower than the cost price he suffers a loss.

Often before selling the goods a shopkeeper spends money in

The shopkeeper adds these overhead expenses to the cost price before he sells the goods at the selling price.

transporting goods keeping goods in good condition Storing the goods in godowns

Total Cost Price = Original Cost Price + Overhead expenses

The money he spends on the above are called overhead expenses.

Therefore,

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When selling price is greater than the cost price the person will earn a profit.(S.P. C.P.)

Selling Price = Cost Price + Profit

Selling Price - Cost Price = Profit

Cost Price = Selling Price - Profit

When cost price is greater than the selling price the person will have a loss. (C.P. S.P.)

Cost Price - Selling Price = Loss

Cost Price = Selling Price + Loss

Selling Price = Cost Price - Loss

With the help of above formulae we can calculate either selling price, cost price, profit or loss.

When there is a profit:

When there is a loss:

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Q.1. Juhi bought a windchime for Rs 385 from Archies Gallery. Kim liked it a lot and asked her to sell it. Jane sold it to Kim for Rs 415.

Cost Price of a wind chime = Rs 385Selling Price of a wind chime = Rs 415

Selling Price – Cost Price = Profit

Rs 415 – Rs 385 = Rs 30

Selling Price > Cost Price , therefore Juhi made a profit.

Did Juhi make profit or loss in this transaction? Calculate the profit or loss.

Ans: Therefore the profit earned by Juhi is Rs 30.

Q.2. Naved bought an umbrella for Rs. 137. After 2 years he sold it for Rs 95.

Cost Price of the umbrella = Rs 137

Selling Price of the umbrella = Rs 95

Cost Price > Selling Price , therefore Naved had a loss.

Cost Price – Selling Price = Loss

Rs 137 – Rs 95

Ans: Therefore Naved suffered a loss by selling his old umbrella.

Did Naved make a profit or had a loss? Calculate the profit or loss?

= Rs 42

cost price, if selling price of an old bicycle is Rs 1975 and the loss on it is Rs 275?

Cost Price = Selling Price + Loss

= Rs 1975 + Rs 275

Ans:The cost price of the bicycle is Rs 2250

selling price, if cost price of a flower vase is Rs 516 and the profit made on it is Rs 96?

Selling Price = Cost Price + Profit = Rs 516 + Rs 96

Ans: The selling price of the flower vase is Rs 612.

= Rs 2250

= Rs 612

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% profit and % loss is always calculated on the cost price.

Percentage profit or percentage loss is calculated on the assumption that the cost price is Rs 100.

Ratio between the cost prices = Ratio between the profits.

Ratio between the cost prices = Ratio between the losses.

Ratio between the cost prices = Ratio between the selling prices.

% of loss =Loss

C.P. 100

% of profit =Profi

t

C.P.

100

We can calculate either selling price, cost price, profit or loss by using “comparison of ratios method”.

Q.1. Tanya bought a Parker pen for Rs 40 and sold it for Rs 48. Calculate

Cost Price of the pen = Rs ___

Selling Price of the pen = Rs ____

Profit = Rs ____– Rs ____ = Rs ___

(Contd…)

Comparison of Ratios Method:

40

48

48 40

8Tanya got a profit of Rs 8 on the cost price of Rs 40.

the profit or loss. the % profit or % loss.

Or = 100 40

Ratio between the cost prices = Ratio between the profits

(By cross multiplication)

Or = 100 40

x8

x8

When we assume that the cost price is 100, then let

the profit made on it be x.

When the cost price of the pen is Rs 40 the profit made on it is Rs 8.

= 100 : 40 x :8

Or = 100 8 x 40 (Contd…

We can calculate % profit by comparing ratios of two cost prices with the ratios of two profits.

Or x =

Or x =

100 8

40

20%

5

1

1

20

Or = 100 8 x 40

Ans: Therefore, Tanya made a profit of 20% by selling the Parker pen.

Original Cost Price = Rs 1730

Overhead expenses = Rs 270

Total C.P. = Original C.P. + Overhead expenses

= Rs 1730 + Rs 270

= Rs 2000

(Contd…)

Q.1. Mrs. Khanna bought a cupboard for Rs 1730. She spent Rs 270 on its transportation. After a few months she sold it for Rs 2500. Calculate the profit or loss.

% profit or % loss.

Therefore, the total cost price of the cupboard is Rs 2000.

Mrs. Khanna made a profit of Rs 500 on the cost price of

Rs 1730. Let x is the profit on cost price of Rs 100.

Ratio between the C.P. = Ratio between the profits

Selling price = Rs 2500

Selling Price – Cost Price = Profit

Rs 2500 – Rs 2000 = Rs 500

Profit = Rs 500

(Contd…)

= 100 2000

x500

x : = 100 : 2000 500

100 x 500 2000

x =

200

2

10 50

x = 25%

20

1 25

1

= 25

Ans:Therefore,Mrs. Khanna made a profit of 25%.

= 100 2000

x500

Q.1. Mr. Raheja bought a camera at Rs 1600. After one year he paid Rs. 400 on its repair and sold it at 5% loss. Calculate the selling price of the camera.Original cost price of the camera = Rs 1600

Overhead expenses (on repair) = Rs 400

Total cost price = Original cost price + Overhead Expenses

= Rs 1600 + Rs 400

Total cost price = Rs 2000

(Contd…)

Mr. Raheja had a loss of 5% by selling the camera.

It means that if Rs 100 be the cost price, the selling price is Rs 100 – Rs 5 = Rs 95

Let x be the S.P. of the camera.

The ratio between the S.P. = The ratio between the C.P.

x 100 = 2000 95

2000 95x = 100= 20 95

x = Rs 1900

Ans: Therefore,selling price of camera was Rs 1900.

1

20

= 2000 100

x95

Selling Price of 1 box of oranges = Rs 88

Selling Price of 10 boxes of oranges = Rs 88

10Selling Price of 10 boxes of oranges = Rs 880

(Contd…)

Q.1. Rima bought 10 boxes of oranges from Nagpur. She spent Rs 50 towards transport. She sold all the 10 boxes of oranges at Rs 88 per box and earned a profit of 10%. Calculate the cost price of each box of oranges?

Rs 880 is the selling price of 10 boxes.

Let x be the cost price of the 10 boxes of oranges.

Ratio between the C.P. = Ratio between the S.P.

Rima made a profit of 10% by selling oranges at Rs 88 per box.

= 880 110

x100

It means that if Rs 100 be the cost price then, selling price is Rs 100 + Rs 10 = Rs 110.

x : 100 880 : 110 =

or x 110 = 880 100 (By cross multiplication)

Rima spent Rs 50 on transportation, therefore the original cost price will be calculated as follows:

x =

880 110

100 x = Rs 800

Cost price of 10 boxes = Rs 800

11

80 10

1

Total cost price = Original cost price + Overhead expenses

Original cost price = Total cost price - Overhead expenses= Rs 800 Rs 50 -= Rs 750

Cost price at which Rima bought 10 boxes of oranges is Rs 750.

Cost price at which Rima bought 1 box = Rs 750

10 1

75

Ans: Therefore the cost price of each box of oranges is Rs 75.

= Rs 75

Jill brought home a poster from her trip to Himachal Pradesh. She had paid Rs 25 for it. Lina saw the poster and liked it. Jill gave it to Lina for Rs 35.

Can you state?• For how many rupee did Jill buy the poster ?

• For how many rupee did Jill sell the poster to Lina ?

• Did Jill make a profit on her transaction, or suffer a loss?

Test YourselfTest Yourself

Ans: Rs 25

Ans: Rs. 35

Ans: Jill made a profit on her transactions.

Complete the table given below:

Test YourselfTest Yourself

175 158 Loss 17

1139 1082 Loss 57

1687 1709 Profit 122

ItemC.P.(Rs.)

S.P.(Rs.)

Amount(Rs.)

Profit / Loss(Rs.)

1.The money at which a shopkeeper buys certain goods is called the cost price of the goods.

2. The money at which a shopkeeper sells the goods is called the selling price of the goods.

4. Selling Price - Cost Price = Profit

5. Cost Price - Selling Price = Loss

6. Selling Price = Cost Price + Profit

7. Cost Price = Selling Price - Profit

9. Cost Price = Selling Price + Loss

8. Selling Price = Cost Price - Loss

3.Total cost price = Original cost price + Overhead Expenses

11. % of loss =Loss

C.P. 100

10. % of profit =Profi

t

C.P.

100

12. Ratio between the cost prices = Ratio between the profits.

13. Ratio between the cost prices = Ratio between the losses.

14. Ratio between the cost prices = Ratio between the selling

prices.

The End Created by:

Department of ResearchBombay Cambridge Gurukul