Chapter 03 Percentages (1) () New Century Mathematics Section Topic Objectives Homework

3.1 Simple Problems Involving Percentages

- Students should be able to use percentage to find a number. - Students should be able to find the percentages (). - Students should be able to convert among fractions, decimals and

percentages. - Students should be able to find the original number from a give percentage.

Ex.3A Q.1-2, 17 Ex.3A Q.5-6 Ex.3A Q.10, 23

3.2 Percentage Change - Students should be able to find the original value, new value, increase / decrease (), percetage increase / decrease (

) and percentage change ().

Ex.3B Q.5-6, 23-24

3.3 Profit and Loss - Students should be to find the cost price (), selling price (), profit / loss () and profit per cent / loss per cent ().

Ex.3C Q.4, 16, 23, 26

3.4 Discount - Students should be able to find the marked price (), selling price, discount () and discount per cent ().

Ex.3D Q.5-7, 22

3.5 Simple Interest - Students should be able to find the principal (), simple interest (), interest rate per annum (), period of time () and amount().

Ex.3E Q.9-12

1. 2. 3. A $3988 B $4088$4000 $300

Chapter 03 Percentages (1) Handout 03-1 F.1_____ Name:______________________________________________( )

unit price

ABC $6.4$6.5 $6.3 1C

25% 25%

28.8% DDC

DDC IDD 25% DDC

DDC DDC IDD $5.70 $5.42 $6.70 $5.70 $5.42 $6.80 $6.60 $6.27 $8.80 $6.10 $5.80 $7.20 $6.90 $6.56 $7.90 $7.10 $6.75 $7.90

$6.20 $5.89 $6.90

DDC

= Y DDC

= Z IDD

= X

= X - YX 100%

= X - ZX 100%

$5.70 $5.42 $6.70 14.9% 19.1% $5.70 $5.42 $6.80 16.2% 20.3% $6.60 $6.27 $8.80 25.0% 28.8% $6.10 $5.80 $7.20 15.3% 19.4% $6.90 $6.56 $7.90 12.7% 17.0% $7.10 $6.75 $7.90 10.1% 14.6%

$6.20 $5.89 $6.90 10.1% 14.6%

F.1 Mathematics Chapter 03 Percentage (1) A. Percentage Increase or Decrease 1. The profit of a company increase from $45 000 last

year to $54 000 this year. What is the percentage increase in profit?

2. The price of a radio decreases from $175 by $70.

What is the percentage decrease in price? 3. A man earns $7200 a month. If his monthly salary

is raised by 10.5%, what is his new salary? 4. The height of a tree was 5.5 m. After one year, the

height of the tree was increased by 12%. Find its new height.

5. There are now 3500 students in a school. If the

number of students is to be increased by 9% next year, how maby students will there be in the school next year?

6. If Mr. Chans salary is increased by 15%, it would

become $10 350. What is his salary? 7. If a certain sum of money is decreased by 10%, it

would become $360. Find the sum of money.

B. Profit and Loss 1. A computer which costs $14 000 is sold at $16 000.

Find (a) the profit, (b) the profit per cent.

2. A department store sold an umbrella at $36. If the umbrella cost $27, find the gain per cent.

3. A chair which costs $80 is sold at $56. Find the

loss per cent. 4. A house which cost $2 100 000 was sold at a loss of

12%. (a) What was the loss in dollars? (b) What was the selling price? 5. An article is bought at $90. If it is sold at a loss of

15%, find the selling price of the article. 6. A book which costs $45 is sold at a profit of 20%. (a) What is the profit? (b) What is the selling price? 7. If a table is sold at $340, the loss per cent is 15%.

Find the cost price of the table.

8. By selling a pen at $51, the loss per cent is 20%.

Find the cost price of the pen. 9. If a shopkeeper sells an article at $6, the gain per cent

is 20%. What will be the selling price if the shopkeeper reduces his gain per cent to 10%?

10. If a calculator was sold at $230, the profit per cent

was 15%. What would be the profit per cent if it was sold at $250?

11. If a machine is sold at $7760, the loss per cent is 3%.

What is the loss per cent if the machine is sold at $7440?

12. A shopkeeper buys 20 dozen eggs for $80. If 4

dozen eggs are rotten and the remaining are sold at $6 per dozen, what is the profit / loss per cent on the whole?

13. A man sells two machines at $9900 each. On one

machine the gain per cent is 10% and on the other the loss is 10%. Find his profit / loss per cent on the whole.

C. Discount 1. Find the discount and the selling price in each of the

following cases: (a) A discount of 10% on a marked price of $90. (b) A discount of 25% on a marked price of $200. (c) A discount of 5% on a marked price of $80. 2. A pair of shoes marked at $180 is sold at discount of

20%. Find the amount of discount. 3. Find the total selling price of 120 pencils which are

marked at 50 each, allowing 10% discount. 4. A chair marked at $70 is sold at a discount of 10%.

What is the selling price? 5. A shirt marked at $125 is sold at $75. Find the

discount and the discount per cent. 6. In a shop, a watch is marked at $200 and a pen is

marked at $180. If Mr. Chan buys the watch at 20% discount and the pen at 15% discount, how much should he pay?

7. A television set was marked at $12 000. A

merchant bought it with a 5% discount. He then sold it and made a profit of 20%. How much did he sell the television set?

8. After a 10% discount, a pen was sold at %5.4. Find

the marked price. 9. An article is marked for sale at $5. The shopkeeper

gives a discount of 5% on this price and still makes a profit of 25%. Find the cost price.

10. The cost price of an article is $15.2. The marked price

is 25% more than the cost price. If the article is sold at 10% discount, what is the selling price?

D. Simple Interest 1. Find the simple interest and the amount on

$250 000 at 3% per annum for 5 years. 2. What is the simple interest on $300 000 at 2.5%

p.a. for 223 years?

3. Find the simple interst on $700 000 for 3 years at

4% per annum. 4. A man depositis $300 000 in a bank at 6% p.a. for

8 months. (a) What is the simple interest? (b) What is the amount received by him? 5. Mr. Chan deposits $1 500 000 in a bank. The

bank pays 2.5% p.a. simple interest. What is the amount received by Mr. Chan after 18 months?

6. Find the amount owed at the end of 6 years by a

man who borrows $5 500 000 at 3.5% p.a. simple interest rate.

7. A man invests $800 000 at 4% p.a. simple interest

rate and $600 000 at 6% p.a. simple interest rate. What is his total annual interest on these investments?

Answers A. Percentage Increase or Decrease 1. 20% 2. 40% 3. $7956 4. 6.16 m 5. 3815 students 6. $9000 7. $400

B. Profit and Lossb

1. (a) $2000 (b) 1427 %

2. 3313 %

3. 30%

4. (a) $252 000 (b) $1 848 000

5. $76.5

6. (a) $9 (b) $54

7. $400

8. $63.75

9. $5.5

10. 25%

11. 7%

12. Profit per cent = 20%

13. Loss per cent = 1%

C. Discount

1.(a) Discount = $9,

selling price = $81

(b) Discount = $50,

selling price price = $150

(c) Discount = $4,

selling price = $76

2. $36

3. $54

4. $63

5. Discount = $50,

discount per cent = 40%

6. $313

7. $13 680

8. $6

9. $3.8

10. $17.1

D. Simple Interest

1. Simple interest = $37 500,

amount = $287 500

2. $20 000

3. $84 000

4. (a) $12 000

(b) $312 000

5. $1 556 250

6. $6 655 000

7. $68 000

Chapter 03 Percentages (1) Quiz 03-1 F.1_____ Name:______________________________________________________( ) Marks:_____/ 43

1. Arrange 13 , 30% and 0.33 in ascending order of

magnitude. (1 mark) 2.(a) Convert 24% into simple fraction.

(b) Convert 0.432 into percentage.

(c) Convert 14 into percentage.

(3 marks) 3. Evaluate (6 marks)

(a) 150 150% 1 + 10% (Express the answer in decimal)

(b) 150% 150% 2 (Express the answer in simple fraction)

(c) 4 + 0.5% 500% 20% (Express the answer in percentage)

4. Solve 2

1 + x% = 4 (3 marks)

5. Find the percentage change when (6 marks) (a) 20 is changed to 25. (b) 25 is decreased by 5. (c) 40 is increased to 60.

30% < 0.33 < 13

24% = 24100

= 625

0.432 = 0.432 100% = 43.2%

14 =

14 100%

= 25%

150 150% 1 + 10%

= 225 1 + 0.1

= 224.1

150% 150% 2

= 32

32 2

= 94 2

= 14

4 + 0.5% 500% 20%

= 400% + 0.5% 100%

= 300.5%

21 + x% = 4

2 = 4 (1 + x%)

0.5 = 1 + x%

x% = 0.5

x = 50

Percentage increase = 25 20

20 100%

= 25%

Percentage decrease = 25 20

25 100%

= 20%

Percentage increase = 60 40

40 100%

= 50%

6. An article has cost price at $10 000. If the shopkeeper raises it by 40% and set as the marked price, and sold it at a discount of 10% off. Find the

(a) marked price (b) discount

(c) selling price (d) profit / loss

(e) profit / loss per cent. (10 marks)

7. A shopkeeper used $250 to buy 500 eggs. (a) Find the cost price of each egg.

(b) The shopkeeper raised 40% of the cost price and set as the marked price. What is the marked price per egg?

(c) If 20% of the eggs are rotten, how many eggs are not rotten?

(d) If the good eggs are sold at the marked price, and 10% discount is given.

(1) What is the total selling price? (2) What is the discount? (3) What is the profit / loss?

(4) What is the profit / loss per cent? (14 marks)

(a) Cost price of each egg = $250 500 = $0.5 (b) Marked price per egg = $0.5 (1 + 40%) = $0.7 (c) Number of rotten eggs = 500 20% = 100 Number of not rotten eggs = 500 100 = 400 (d)(1) Total selling price

= $0.7 (500 100) (1 10%) = $252

(2) Discount = $0.7 (500 100) - $252 = $28 (3) Profit = $252 $250 = $2

(4) Profit per cent = 2

250 100% = 0.8%

(a) Marked price = $10 000 (1 + 40%)

= $14 000

(b) Discount = $14 000 10% = $1 400

(c) Selling price = $14 000 $1 400

= $12 600

(d) Profit = $12 600 $10 000

= $2 600

(e) Profit percentage = 2 60010 000 100%

= 26%

Chapter 03 Percentages (1) Quiz 03-2 F.1_____ Name:______________________________________________________( ) Marks:_____/ 32 1. Peter bought an article for $x. He sold it to Mary

at a profit of 20%. Mary then sold it to John for $90 at a loss of 25%. Find x.

A. 56.25 B. 81 C. 90 D. 100 E. 144 2. By selling an article at 10% discount off the marked

price, a shop still makes 20% profit. If the cost price of the article is $19 800, then the marked price is

A. $21 600 B. $26 136 C. $26 400 D. $27 225 E. $27 500

3. The marked price of a toy is $120 and the percentage profit is 60%. If the toy is sold at a discount of 20%, the profit is

A. $14.40 B. $21.00 C. $24.00 D. $33.60 E. $48.00 4. If a dictionary is sold at its marked price, then the

percentage profit is 30%. If the dictionary is sold at a 20% discount on its marked price, then the profit is $5. Find the cost of the dictionary.

A. $104 B. $105 C. $125 D. $130

5.(a) A man deposited $50 000 in a bank at an interest rate of 6% per annum simple interest. After several years, he got back $65 000. Find the time taken.

(b) If he put $50 000 in another bank at an interest rate of 5% p.a. simple interest. After 2 years, find

(1) the total simple interest, and (2) the amount

he would get back from the second bank. (6 marks)

(a) Time taken = 65 000 50 000

50 000 6% years

= 5 years

(b)(1) Total simple interest = $50 000 5% 2 = $5 000

(2) Amount = $50 000 + $5 000

= $55 000

6. Peter invested $50 000 in Bank A at 4% p.a. simple interest. Find

(a) the interest after half year, and (b) the amount he could get back after half year. If after half year, he took out all money and

deposited in Bank B, he would get back $54 000 after another year. Find

(c) the interest rate of Bank B per annum, and (d) the total time needed that the amount he got

would be twice the principal he put in Bank B. (8 marks)

7.(a) Mary deposited a certain amount of money in a bank at a rate at 5% per annum. After 2 years, she got back $110 000, find

(1) the principal, and (2) the simple interest. (b) She took out all the amount and buy an article.

She set 20% more as the marked price, what is the marked price?

(c) She then gave a 40% discount. Find (1) the discount, (2) the selling price,

(3) her final profit / loss for the sale, and (4) the profit / loss per cent for the sale.

(14 marks)

(a)(1) Principal = $110 000

1 + 5% 2

= $100 000

(2) Simple interest = $110 000 $100 000

= $10 000

(b) Marked price = $110 000 (1 + 20%)

= $132 000

(c)(1) Discount = $132 000 40% = $52 800

(2) Selling price = $132 000 $52 800

= $79 200

(3) Loss for the sale = $110 000 $79 200

= $30 800

(4) Loss percentage = 30 800110 000 100%

= 28%

(a) Simple interest after half year = $50 000 4% 0.5 = $1 000 (b) Amount he could get back after half year = $50 000 + $1 000 = $51 000 (c) Interest rate per annum

= 54 000 51 000

51 000 0.5 100%

= 111317 %

(d) He can get $3 000 per half year, and he needs 8.5 years to double the principal.