F

F.1 Mathematics Supplementary Notes Chapter 6 Percentage (I)

2/2002 P. 12

Chapter 6 Percentage(I)

Name:___________( ) Class: F.1 ( ) Important Terms

percentage increaseprofit

percentage decreaseloss

marked pricediscount

selling price / cost

Revision Notes

1. Percentage Change

(a)Increase = New value Original value

Percentage increase =

New value = Original value(1+Percentage increase)

(b)Decrease = Original value New value

Percentage decrease =

New value = Original value(1Percentage decrease)

(c)Percentage change =

Example:

What is 20% of 250 ?

20% of 250

= 50

Example: The percentage increase when 100 is increased to 150

=

= 50%

Example:

Find the result when the number 200 is

(a)increased by 15%

(b)decreased by 30.5%

Solution:

(a)the new number = 200(1+15%) = 200

= 230

(b)the new number =200(130.5%) = 200

= 139

2.Profit and Loss

(a)Profit = Selling price Cost price

Profit % =

Profit = Cost priceProfit %

Selling price = Cost price(1+ Profit %)

(b)Loss = Cost price Selling price

Loss % =

Loss = Cost priceLoss %

Selling price = Cost price(1Loss %)

Example:

A T-shirt which cost $100 is sold at $105 ,

the profit % =

= 5%

Example:

A toy which is bought at $100 is sold at $80,

the loss% =

= 20%

3.Discount

Discount =Marked price Selling price

Discount % =

Example:

A handbag marked at $220 is sold at $187.

Discount= $220 $187

= $33

Discount%=

= 15%

Exercise A (Level I)1.Complete the following table.

Original valueNew valueIncrease / DecreasePercentage change

144a decrease of 36

61.5an increase 24

6378.75

16.59.9

575%

an increase 28+40

2.What percentage of 24 is 18?

3.(a)What is 125% of 50 kg ?

(b).What percentage of $30 is $1.5 ?

4.40% of a class of 50 students are girls. How many boys are there in the class.

5.140 students sit for a test. 85% of them pass the test. How many students pass the test ?

6.There are 40 students in a class. 15 of them are boys. What percentage of the students in the class are boys ?

7.In a class of 50 students, 2 of them are absent (). What is the percentage of students who are present () ?8.John is 12 years old and Peter is 16 years old. What percentage of Peter's age is John's age ?

9.The price of a calculator is increased from $200 to $250.What is the percentage increase ?

10.If John's salary is increased by 15%, it would become $10350. What is his salary now ?

11.The length of a stick is 60cm. If its length is changed by (30%, what will be the new length?

12.15% of a number is 24. What is the original number.Solution :Let the original number be n.

13.Mr. Chan saves $680, and it is 8.5% of his monthly salary. Whatis his monthly salary ?

( Level II )

14.25% of a number is equal to 40% of 35, find the original number.

15.25% of a sum of money is $35. Find 6.5% of the sum of money.

16.In a test, 45% of the students failed. If 99 students passed, how many students sat for the test ?

17.After walking 54km, a man estimates that he still has 70% of hisjourney to go. What is the total distance of his journey ?

18.x is 100. y is 30% of x, and y is 150% of z. What is z?

19.Given a fraction . If the numerator () is increased by 20%, find

(a)the new fraction,

(b)the percentage increase in the value of the fraction.

20.(a)In figure (a), the length of the rectangleis 15cm, and the width is 6cm.

Find the area of the rectangle.

(b)If the length is decreased by 20%, and the width is increased by 50%

as shown in figure (b), find

(i)the new length of the rectangle

(ii)the new width of the rectangle

(iii)the new area of the rectangle

(c)Find the percentage change in area of the rectangle.

Exercise B (Level I )1.Complete the following table

Cost

priceSelling

priceProfitPercentage

profitRough Work ()

(a)$10

$20

(b)$150$30

(c)$88

10%

(d)

$220

$120

(e)

$10

15%

2.Complete the table

Cost

priceSelling

priceLossPercentage

lossRough Work ()

(a)$60

5%

(b)$3500

$500

(c)$2500

$100

(d)$120

$80

(e)

$15.5

10%

3.Mary bought a car for $200 000. She sold it to John at a loss of $25 000. Find

(a)the selling price of the car,

(b)Mary's percentage loss.

4.A house which cost $4 800 000 was sold at a loss of 7%.

(a)What was the loss ?

(b)What was the selling price?

5.A hawker bought 100 pieces of articles at $48 a piece. He sold all thearticles and made a profit of $6 a piece. Find

(a)the selling price of a piece of article,

(b)the percentage profit.

( Level II )

6.David sold 10 stamps to Ricky at a profit of 10%, then Ricky sold them to May at a profit of 20%. If May paid $264 for the stamps, find

(a)the amount David paid for the stamps;

(b)the profit that Ricky made on each stamp.

7.A sold his car to B at a loss of 20%. B sold it to C at a profit of 5%. If C paid $168 000 for the car, find As loss.

Excrcise C (Level I )

1.Complete the following table.

Marked

priceSelling

priceDiscountPercentage

discountRough Work ()

(a)$1200

5%

(b)$4.216%

(c)$16

$2

(d)$200$120

(e)$1.9$0.1

(f)$500

$80

(g)

$8424%

2.When a book is sold at a 10% discount, the discount is $6. What is the marked price and the selling price of this book?

3.A department store gives a 15% discount on all items during the grand reduction. How much would John have to pay for a watch marked $260.

4.The marked price of a television was $3360 after it had been raised by 12% of the original price.

(a)Find the original price.

(b)If a 12% discount was given to the marked price, what was the selling price.

( Level II )

5.In a shop, a watch is marked at $200 and a pen is marked at $180. If John buys the watch at 20% discount and the pen at 15% discount, how much should he pay?

6.Tickets for a concert are $140, but for a group of 15 or more there is a discount of 15%. John organizes a group of 18 of his classmates to go tothe concert. What is the total cost of the tickets?7.A discount of 8% is given to a customer who pays in cash. Suppose Tom wants to buy an article which costs $45000.

(a)How much money is saved if he pays in cash?

(b)How much more can he save if the discount is 9%?

Level III (*Optional)

1.John is 40% heavier than Ruby, and Ruby is 30% lighter than Peter. The weight of Ruby is 42 kg.

(a)Find the respective weights of John and Peter.

(b)Between John and Peter, who is lighter? By what percentage?

(Ans. (a) 58.8kg 60kg (b)2%)

2.A man sells two photocopy machines at $198 000 each. He makes a profit of 10% on one machine and suffers a loss of 10% on the other. On the whole, find

(a)his profit or loss;

(b)his profit % or loss %.

(Ans. (a)Loss $400 ; (b)Loss 1%)

3.The marked price of an article is 60% above its cost price. In a sale, it is sold at a discount of x% .

Find x if the profit can still be kept at 44%.

(Ans. 10)

4.A store-keeper sets the price of his goods at 25% above their cost price. If he wants to sell his goods to his friend at the cost price, find the percentage discount that he would allow.

(Ans.20%)

5.The water in a tank has increased by 20% and then 25% was used. What was the overall percentage change in volume ?

(Ans.10%)

6.

m% n% ;

n% m% ;

;

mn,

()

7.6120.01472

($0.57)

8.1000200

1000150

20010

1065%35%

10

(480%)

9. 1 23cm13cm98%

(4*13cm +2*23cm)

In general, if we want to find out what percentage of y is x, we can first form the fraction EMBED Equation.3 , then convert it into a percentage.

Figure (b)

Figure (a)

6cm

15cm

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