Mathem atics Std: 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,

Important Formulae  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: > >

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 385 Selling 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 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 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 Rs 96 Ans: The selling price of the flower vase is Rs 612. = Rs 2250 = Rs 612

Important Formulae % 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 = Profit 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: Tanya got a profit of Rs 8 on the cost price of Rs 40.  the profit or loss.  the % profit or % loss.

Or = Ratio between the cost prices = Ratio between the profits (By cross multiplication) Or = x 8 x 8 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 = 100  % 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 Rs 270 = Rs 2000 (Contd…) Q.1. Mrs. Khanna bought a cupboard for Rs She spent Rs 270 on its transportation. After a few months she sold it for Rs 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 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…)  = x 500 x :  = 100 :

100 x x =  x = 25% = 25 Ans: Therefore,  Mrs. Khanna made a profit of 25%.  = x 500

Q.1. Mr. Raheja bought a camera at Rs 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 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 x = 100 = 20  95  x = Rs 1900 Ans: Therefore,  selling price of camera was Rs = x 95

Selling Price of 1 box of oranges = Rs 88  Selling Price of 10 boxes of oranges = Rs 88  10  Selling 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.  = x 100 It means that if Rs 100 be the cost price then, selling price is Rs Rs 10 = Rs 110. x : : 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=x=    x = Rs 800 Cost price of 10 boxes = Rs 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  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 Yourself Ans: Rs 25 Ans: Rs. 35 Ans: Jill made a profit on her transactions.

Complete the table given below: Test Yourself Loss Loss Profit122 Item C.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.  % of profit = Profit C.P.  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 Research Bombay Cambridge Gurukul