SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Ratio, SM-Bank 038

Damon buys 25 kilograms of salt for his pool for $33.75.

The salt can be purchased in 1 kilogram bags.

How much does 9 kilograms of salt cost?  (2 marks)

Show Answers Only

\($12.15\)

Show Worked Solution

\(\text{C}\text{ost of 1 kilogram}\)

\(=\dfrac{33.75}{25}\)

\(= $1.35\)
 

\(\therefore\ \text{C}\text{ost of 9 kilograms}\)

\(= 9\times 1.35\)

\(= $12.15\)

Ratio, SM-Bank 037 MC

Tony is making a fruit cake.

The recipe says he needs 3 cups of sultanas for every 5 cups of flour.

If 2.5 cups of flour are used, how many cups of sultanas are needed?
 

  1. \(0.5\ \text{cups}\)
  2. \(1.5\ \text{cups}\)
  3. \(2.5\ \text{cups}\)
  4. \(4.5\ \text{cups}\)
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Strategy 1:}\)

\(2.5\ \text{ is half of }\ 5\ \text{cups of flour, therefore half of}\)

\(3\ \text{cups of sultanas is required.}\)

\(\rightarrow\ 1.5\text{ cups of sultanas needed.}\)

 

\(\text{Strategy 2:}\)

\(\text{Let}\ \ n = \text{cups of sultanas needed}\)

\(\dfrac{n}{2.5}\) \(=\dfrac{3}{5}\)
\(\therefore \ n\) \(=\dfrac{3\times 2.5}{5}\)
  \(=1.5\ \text{cups}\)

 
\(\Rightarrow\ B\)

Ratio, SM-Bank 036

Milly is using this cupcake recipe.
 

 How many cups of sugar are needed for 20 cupcakes?  (2 marks)

Show Answers Only

\(3\dfrac{3}{4}\ \text{cups}\)

Show Worked Solution

\(\text{From the recipe:}\)

\(\dfrac{3}{4}\ \text{cups} = 4\ \text{cupcakes}\)

\(\therefore\ \text{Sugar in 20 cupcakes}\) \(=\dfrac{3}{4}\times 5\)
  \(=\dfrac{15}{4}\)
  \(=3\dfrac{3}{4}\ \text{cups}\)

Ratio, SM-Bank 035 MC

The actual body length of a beetle Brad has caught is 24 mm.

A scale drawing of the beetle is shown below.

What scale is used in the drawing?

  1. \(1 \text{cm represents } 5\ \text{mm}\)
  2. \(1 \text{cm represents } 2\ \text{mm}\)
  3. \(2 \text{cm represents } 1\ \text{mm}\)
  4. \(5 \text{cm represents } 1\ \text{mm}\)
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Scale:}\)

\(12\ \text{cm}: 24\ \text{mm}\) \(=120\ \text{mm}: 24\ \text{mm}=5:1\)

  
\(\text{In the options given, the ratio of}\ 5 : 1\ \text{occurs when}\)

\(\text{10 mm represents 2 mm}\ \textbf{OR}\ \text{when 1 cm represents 2 mm}\)
  

\(\Rightarrow B\)

Ratio, SM-Bank 034 MC

This picture shows a stone vase.
 

 
The picture is 2 cm high. The actual vase is 40 cm high.

What scale is used in the picture?

  1. \(\text{2 cm represents 20 cm}\)
  2. \(\text{4 cm represents 40 cm}\)
  3. \(\text{1 cm represents 2 cm}\)
  4. \(\text{1 cm represents 20 cm}\)
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Scale:}\ \ 2\ \text{cm}\ :\ 40\ \text{cm}\)

\(\rightarrow \text{Divide both sides by }2\)

\(\text{Scale:}\ \ 1\ \text{cm}\ :\ 20\ \text{cm}\)

 
\(\Rightarrow D\)

Ratio, SM-Bank 033 MC

Two places are 5.4 cm apart on a map.

On the map 1 cm represents 4 km.

What is the actual distance between the two places?

  1. \(1.08\ \text{km}\)
  2. \(10.8\ \text{km}\)
  3. \(21.6\ \text{km}\)
  4. \(43.4\ \text{km}\)
Show Answers Only

\(C\)

Show Worked Solution
\(\text{Actual distance}\) \(=5.4\times 4\)
  \(=21.6\ \text{km}\)

 
\(\Rightarrow C\)

Ratio, SM-Bank 032 MC

Shelley and Carly collect dolls.

The ratio of the number of dolls Shelley owns compared to Carly is  3 : 2.

Shelley owns 12 dolls.

How many dolls does Carly own?

  1. \(2\)
  2. \(6\)
  3. \(8\)
  4. \(18\)
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Shelley’s dolls represents 3 parts}\)

\(3\ \text{parts}\) \(=12\)
\(1\ \text{part}\) \(=\dfrac{12}{3}=4\)

    
\(\text{Carly’s dolls represents 2 parts}\)

\(=2\times 4=8\)
 

\(\therefore\ \text{There Carly owns}\ 8\ \text{dolls.}\)
 

\(\Rightarrow C\)

Ratio, SM-Bank 031

Jordan has 4 times as many blue pencils as black pencils.

Altogether he has 90 pencils.

How many blue pencils does he have?  (2 marks)

Show Answers Only

\(72\ \text{blue pencils}\)

Show Worked Solution

\(\text{Method 1}\)

\(\text{Ratio of blue to black}=4:1\)

\(\text{Total parts}=4+1=5\)
  

\(\text{Fraction blue}=\dfrac{4}{5}\)

\(\text{Number of blue pencils}=\dfrac{4}{5}\times 90=72\)
  

\(\text{Method 2 (Advanced)}\)

\(\text{Let}\ \ x = \text{the number of black pencils}\)

\(\text{Then the number of blue pencils}=4x\)

\(\text{Total pencils }= x + 4x\) \(=5x\)
\(\rightarrow\ 5x\) \(= 90\)
\(x\) \(=\dfrac{90}{5}= 18\)

 

\(\therefore \ \text{The number of blue pencils}\)

\(=90-18= 72\)

Ratio, SM-Bank 029 MC

A television broadcasting tower is 800 metres high.

A model of the tower is built with a scale of  1 : 4000.

What is the height of the model?

  1. \(5\ \text{cm}\)
  2. \(20\ \text{cm}\)
  3. \(200\ \text{cm}\)
  4. \(320\ \text{cm}\)
Show Answers Only

\(B\)

Show Worked Solution
\(\text{Model height}\) \(=\dfrac{800}{4000}\)
  \(= 0.2\ \text{m}\)
  \(= 20\ \text{cm}\)

 
\(\Rightarrow B\)

Ratio, SM-Bank 028 MC

A little athletics club is established in a town.

In the first week, 5 girls and 6 boys joined the club.

In the second week, another 4 boys and some more girls joined the club.

The number of girls in the club was now double the number of boys.

How many girls joined the club in the second week?

  1. \(7\)
  2. \(15\)
  3. \(17\)
  4. \(20\)
Show Answers Only

\(B\)

Show Worked Solution

\(\text{1st week}\rightarrow 6\ \text{boys.}\)

\(\text{2nd week }\rightarrow 6+4 = 10\ \text{boys.}\)

\(\text{Total girls in 2nd week.}\)

\(= 2\times 10\)

\(= 20\)
 

\(\therefore\ \text{Girls joining in 2nd week.}\)

\(= 20-5\)

\(= 15\)
 

\(\Rightarrow B\)

Ratio, SM-Bank 027 MC

Muriel made a batch of cookies.
 

 
Each cookie had 4 chocolate chips and 3 jelly snakes on it.

Muriel used 39 jelly snakes in the batch of cookies.

How many chocolate chips did she use?

  1. \(13\)
  2. \(26\)
  3. \(52\)
  4. \(78\)
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Number of cookies made}\)

\(=\dfrac{39}{3}\)

\(=13\)

\(\therefore\ \text{Chocolate chips used}\)

\(=13\times 4\)

\(=52\)

 
\(\Rightarrow C\)

Ratio, SM-Bank 026

It is known that one of the angles in a triangle is \(120^{\circ}\).

Calculate the size of the other 2 angles if they are in the ratio \(2:3\).  (3 marks)

Show Answers Only

\(24^{\circ}\ \text{and}\ 36^{\circ}\)

Show Worked Solution

\(\text{Angle sum of a triangle}=180^{\circ}\)

\(\therefore\ \text{Remaining angles}=180-120=60^{\circ}\)

\(\text{Total parts remaining angles}=2+3=5\)    

\(\text{1st angle}=\dfrac{2}{5}\times 60=24\)

\(\text{2nd angle}=\dfrac{3}{5}\times 60=36\)
    

\(\therefore\ \text{The remaining angles are}\ 24^{\circ}\ \text{and}\ 36^{\circ}.\)

Ratio, SM-Bank 025

The ratio of the angles in a triangle is 1:2:5.

Calculate the sizes of all three angles?  (2 marks)

Show Answers Only

\(22.5^{\circ}, 45^{\circ} \text{ and}\ 112.5^{\circ}\)

Show Worked Solution

\(\text{Total parts}=1+2+5=8\ \text{and the angle sum of a triangle}=180^{\circ}\)

\(\dfrac{1}{8}\times 180\) \(=22.5\)
\(\dfrac{2}{8}\times 180\) \(=45\)
\(\dfrac{5}{8}\times 180\) \(=112.5\)

    
\(\therefore\ \text{The angles in the triangle are }22.5^{\circ}, 45^{\circ} \text{ and}\ 112.5^{\circ}\)

Ratio, SM-Bank 024

Joe and Andrew are cleaning fish. For every 4 fish that Joe cleans, Andrew cleans 7.

If Joe cleaned 36 fish, how many did Andrew clean?  (2 marks)

Show Answers Only

\(63 \text{ fish}\)

Show Worked Solution

\(\text{Joe’s cleaned fish represents 4 parts}\)

\(4\ \text{parts}\) \(=36\)
\(1\ \text{part}\) \(=\dfrac{36}{4}=9\)

    
\(\text{Andrew’s cleaned fish represents 7 parts}\)

\(=9\times 7=63\)
 

\(\therefore\ \text{Andrew cleaned}\ 63\ \text{fish.}\)

Ratio, SM-Bank 023

This year there are 108 students in Year 8 and the ratio of Year 7 students to Year 8 students is 8:9.

Use this information to calculate the number of students in Year 7 this year.  (2 marks)

Show Answers Only

\(96 \text{ students in Year 7}\)

Show Worked Solution

\(\text{Year 8 represents 9 parts}\)

\(9\ \text{parts}\) \(=108\)
\(1\ \text{part}\) \(=\dfrac{108}{9}=12\)

    
\(\text{Year 7 represents 8 parts}\)

\(=12\times 8=96\)
 

\(\therefore\ \text{There are}\ 96\ \text{students in Year 7.}\)

Ratio, SM-Bank 022

Divide $420 in the ratio 1:3:2.  (2 marks)

Show Answers Only

\($70, $210 \text{ and } $140\)

Show Worked Solution

\(\text{Total number of parts}=1+3+2=6\)

\(\dfrac{1}{6}\times 420\) \(=70\)
\(\dfrac{3}{6}\times 420\) \(=210\)
\(\dfrac{2}{6}\times 420\) \(=140\)

  
\(\therefore\ $420\ \text{divided in the ratio }\ 1:3:2\ \text{ is }\ $70, $210\ \text{and } $140.\)

Ratio, SM-Bank 021

Divide 84 days in the ratio 3:4.  (2 marks)

Show Answers Only

\(36\ \text{days and } 48\ \text{days}\)

Show Worked Solution

\(\text{Total number of parts}=3+4=7\)

\(\dfrac{3}{7}\times 84\) \(=36\)
\(\dfrac{4}{7}\times 84\) \(=48\)

  
\(\therefore\ 84\ \text{days divided in the ratio }3:4\ \text{is }36\ \text{days and } 48\ \text{days.}\)

Ratio, SM-Bank 020

Divide 480 tonnes in the ratio 1:5.  (2 marks)

Show Answers Only

\(80\ \text{tonnes and}\ 400\ \text{tonnes}\)

Show Worked Solution

\(\text{Total number of parts}=1+5=6\)

\(\dfrac{1}{6}\times 480\) \(=80\)
\(\dfrac{5}{6}\times 480\) \(=400\)

  
\(\therefore\ 480\ \text{tonnes divided in the ratio }1:5\ \text{is }80\ \text{tonnes and } 400\ \text{tonnes.}\)

Ratio, SM-Bank 019

Divide $130 in the ratio 5:8.  (2 marks)

Show Answers Only

\($50\ \text{and}\ $80\)

Show Worked Solution

\(\text{Total number of parts}=5+8=13\)

\(\dfrac{5}{13}\times 130\) \(=50\)
\(\dfrac{8}{13}\times 130\) \(=80\)

  
\(\therefore\ \$130\ \text{divided in the ratio }5:8\ \text{is }$50\ \text{and}\ $80.\)

Ratio, SM-Bank 018

The ratio of kilograms of bananas to apples at the fruit shop is \(11:5\).

  1. What fraction of the fruit is bananas?  (1 mark)

  2. If there are 128 kilograms of bananas and apples altogether, how many kilograms of bananas are there?  (2 marks)

Show Answers Only

a.    \(\dfrac{11}{16}\)

b.    \(88\ \text{kg of bananas}\)

Show Worked Solution

a.    \(\text{Total fruits}=11+5=16\)

\(\text{Fraction bananas}=\dfrac{11}{16}\)
 

b.   
\(\text{Kilograms of bananas}\) \(=\dfrac{11}{16}\times 128\)
    \(=88\)

 
\(\therefore\ \text{There are }88\ \text{kgs of bananas.}\)

Ratio, SM-Bank 017

The ratio of dogs to cats in an animal rescue shelter is \(5:4\).

  1. What fraction of the animals are dogs?  (1 mark)

  2. What fraction of the animals are cats?  (1 mark)

  3. If there are 36 animals in the shelter, how many are dogs?  (2 marks)

Show Answers Only

a.    \(\dfrac{5}{9}\)

b.    \(\dfrac{4}{9}\)

c.    \(20\ \text{dogs}\)

Show Worked Solution

a.    \(\text{Total animals}=5+4=9\)

\(\text{Fraction dogs}=\dfrac{5}{9}\)
 

b.    \(\text{Fraction cats}=\dfrac{4}{9}\)

 

c.   
\(\text{Number of dogs}\) \(=\dfrac{5}{9}\times 36\)
    \(=20\)

 
\(\therefore\ \text{There are }20\ \text{dogs in the shelter.}\)

Ratio, SM-Bank 016

Maude has 55 cents in coins and Will has $2.70 in coins.

  1. Write Maude's money as a ratio of Will's money in cents.  (1 mark)

  2. Express the ratio in simplest form.  (2 marks)

Show Answers Only

a.    \(55:270\) 

b.    \(11:54\)

Show Worked Solution
a.    \(55\ \text{cents to}\ $2.70\) \(=55:270\)

 

b.    \(55:270\) \(=\dfrac{55}{5}:\dfrac{270}{5}\)
    \(=11:54\)

Ratio, SM-Bank 015

Change these ratios to the same units and then write in simplest form.

  1. \(40\ \text{cm}: 1.2\ \text{m}\)  (2 marks)

  2. \(4\ \text{hours}:20\ \text{minutes}\)  (2 marks)

  3. \(15\ \text{days}: 3\ \text{weeks}\)  (2 marks)

Show Answers Only

a.    \(1:3\) 

b.    \(6:1\)

c.    \(5:7\)

Show Worked Solution
a.    \(40\ \text{cm}:1.2\ \text{m}\) \(=40\ \text{cm}:120\ \text{cm}\)
    \(=40:120\)
    \(=1:3\)

 

b.    \(4\ \text{hours}:20\ \text{minutes}\) \(=240\ \text{minutes}:40\ \text{minutes}\)
    \(=240:40\)
    \(=6:1\)

 

c.    \(15\ \text{days}:3\ \text{weeks}\) \(=15\ \text{days}:21\ \text{days}\)
    \(=15:21\)
    \(=5:7\)

Ratio, SM-Bank 014

Fully simplify the following ratios.

  1. \(\dfrac{5}{12}:\dfrac{11}{8}\)  (2 mark)

  2. \(1\dfrac{1}{4}:3\dfrac{1}{2}\)  (2 marks)

Show Answers Only

a.    \(10:33\) 

b.    \(5:14\)

Show Worked Solution
a.    \(\dfrac{5}{12}:\dfrac{11}{8}\) \(=\bigg(\dfrac{5}{12}\times 24\bigg):\bigg(\dfrac{11}{8}\times 24\bigg)\) \(\ \ \text{Multiply by LCM of 12 and 8.}\)
    \(=10:33\)  

 

b.    \(1\dfrac{1}{4}:3\dfrac{1}{2}\) \(=\dfrac{5}{4}:\dfrac{7}{2} \ \ \ \text{Convert to improper fractions }\)
    \(=\bigg(\dfrac{5}{4}\times 4\bigg):\bigg(\dfrac{7}{2}\times 4\bigg)\ \ \ \ \text{Multiply by LCM of 4 and 2. }\)
    \(=5:14\)

Ratio, SM-Bank 013

Fully simplify the following ratios.

  1. \(\dfrac{1}{2}:3\)  (1 mark)

  2. \(\dfrac{1}{4}:\dfrac{1}{3}\)  (2 marks)

Show Answers Only

a.    \(1:6\) 

b.    \(3:4\)

Show Worked Solution
a.    \(\dfrac{1}{2}:3\) \(=\Bigg(\dfrac{1}{2}\times 2\Bigg):\Bigg(3\times 2\Bigg)\) \(\ \ \text{Multiply by LCM of 2 and 1.}\)
    \(=1:6\)  

 

b.    \(\dfrac{1}{4}:\dfrac{1}{3}\) \(=\Bigg(\dfrac{1}{4}\times 12\Bigg):\Bigg(\dfrac{1}{3}\times 12\Bigg)\) \(\ \ \text{Multiply by LCM of 3 and 4. }\)
    \(=3:4\)  

Ratio, SM-Bank 012

Fully simplify the following ratios.

  1. \(10:32\)  (1 mark)

  2. \(144:60\)  (1 mark)

  3. \(36:18:66\)  (1 mark)

Show Answers Only

a.    \(5:16\) 

b.    \(12:5\)

c.    \(6:3:11\)

Show Worked Solution
a. \(10:32\) \(=\dfrac{10}{2}:\dfrac{32}{2}\) \(\ \ \text{(Divide by HCF of 10 and 32.)}\)
    \(=5:16\)  

 

b. \(144:60\) \(=\dfrac{144}{12}:\dfrac{60}{12}\) \(\ \ \text{(Divide by HCF of 144 and 60.)}\)
    \(=12:5\)  

 

c. \(36:18:66\) \(=\dfrac{36}{6}:\dfrac{18}{6}:\dfrac{66}{6}\) \(\ \ \text{(Divide by HCF of 36, 18 and 66.) }\)
    \(=6:3:11\)  

Ratio, SM-Bank 011

Fully simplify the following ratios.

  1. \(24:18\)  (1 mark)

  2. \(180:81\)  (1 mark)

  3. \(14:49:56\)  (1 mark)

Show Answers Only

a.    \(4:3\) 

b.    \(20:9\)

c.    \(2:7:8\)

Show Worked Solution
a.    \(24 :18\) \(=\dfrac{24}{6}:\dfrac{18}{6}\) \(\ \ \text{(Divide by HCF of 24 and 18.)}\)
    \(=4:3\)  

 

b.    \(180 :81\) \(=\dfrac{180}{9}:\dfrac{81}{9}\) \(\ \ \text{(Divide by HCF of 180 and 81.)}\)
    \(=20:9\)  

 

c.    \(14 :49:56\) \(=\dfrac{14}{7}:\dfrac{49}{7}:\dfrac{56}{7}\) \(\ \ \text{(Divide by HCF of 14, 49 and 56.)}\)
    \(=2:7:8\)  

Ratio, SM-Bank 008

Complete each pair of equivalent ratios.  (3 marks)

a.    
\(16:12=\)
  
 \(:3\)
b.
 \(18:24=\)
  
 \(:4\)
c. \(54:9=\)
  
 \(:1\)
Show Answers Only

a.    \(4:3\)

b.    \(3:4\)

c.    \(6:1\)

Show Worked Solution
a.    \(16 :12\) \(=(16÷4):(12÷4)\)
  \(=4:3\)

 

b.    \(18 :24\) \(=(18÷6):(24÷6)\)
  \(=3:4\)

 

c.    \(54 :9\) \(=(54÷9):(9÷9)\)
  \(=6:1\)

Ratio, SM-Bank 007

Complete each pair of equivalent ratios.  (3 marks)

a.    \(3:4\) \(=9:\)
 
b.    \(2:5\)
 \(=8:\)
  
c.    \(10:3\)
 \(=30:\)
  
Show Answers Only

a.    \(9:12\)

b.    \(8:20\)

c.    \(30:9\)

Show Worked Solution
a.    \(3 :4\) \(=3\times 3:4\times 3\)
  \(=9:12\)

 

b.    \(2 :5\) \(=2\times 4:5\times 4\)
  \(=8:20\)

 

c.    \(10 :3\) \(=10\times 3:3\times 3\)
  \(=30:9\)

Ratio, SM-Bank 006 MC

At the Year 7 camp, there were 20 teachers and 180 students.

What is the ratio of students to the total number of people at the camp?

  1. \(9:2\)
  2. \(180:20\)
  3. \(9:10\)
  4. \(9:1\)
Show Answers Only

\(C\)

Show Worked Solution
\(\text{students}\ :\ \text{total}\) \(=180:(20+180)\)
  \(=180:200\)
  \(=9:10\)

 
\(\Rightarrow C\)

Ratio, SM-Bank 003

James was building a lego house and has the pieces below left over.

Calculate:

  1. the ratio of blue bricks to yellow.  (1 mark)

  2. the ratio of pink bricks to the total leftover bricks.  (1 mark)

  3. the ratio of yellow bricks to other leftover bricks.  (1 mark)

Show Answers Only

a.    \(4:5\)

b.    \(2:11\)

c.    \(5:6\)

Show Worked Solution

a.    \(\text{Blue}:\text{Yellow}=4:5\)

b.    \(\text{Total Bricks}=2+4+5=11\)

\(\text{Pink}:\text{Total}=2:11\)

c.    \(\text{Total other bricks}=2+4=6\)

\(\text{Yellow}:\text{Other}=5:6\)

Ratio, SM-Bank 002

A fruit bowl contains 8 apples, 7 bananas, 1 pear and 13 oranges.

Calculate:

  1. the ratio of apples to oranges.  (1 mark)

  2. the ratio of oranges to the total pieces of fruit in the bowl.  (1 mark)

  3. the ratio of pears to other pieces of fruit.  (1 mark)

Show Answers Only

a.    \(8:13\)

b.    \(13:29\)

c.    \(1:28\)

Show Worked Solution

a.    \(\text{Apples}:\text{Oranges}=8:13\)

b.    \(\text{Total Fruit}=8+7+1+13=29\)

\(\text{Oranges}:\text{Total}=13:29\)

c.    \(\text{Total other fruit}=8+7+13=28\)

\(\text{Pear}:\text{Other}=1:28\)

Ratio, SM-Bank 001

A bag contains 3 red marbles, 4 blue marbles and 8 white marbles.

Calculate:

  1. the ratio of red marbles to blue marbles.  (1 mark)

  2. the ratio of white marbles to the total number of marbles.  (1 mark)

  3. the ratio of blue marbles to other colours.  (1 mark)

Show Answers Only

a.    \(3:4\)

b.    \(8:15\)

c.    \(4:11\)

Show Worked Solution

a.    \(\text{Red}:\text{Blue}=3:4\)

b.    \(\text{Total marbles}=3+4+8=15\)

\(\text{White}:\text{Total}=8:15\)

c.    \(\text{Total other marbles}=3+8=11\)

\(\text{Blue}:\text{Other}=4:11\)

Percentages, SM-Bank 089

Calculate the percentage discount on an item having a cost price of $45 and a sale price of $30.15. (2 marks)

Show Answers Only

\(33\text{%}\)

Show Worked Solution
 \(\text{Discount}\) \(=\text{Cost Price}-\text{Sale Price}\)
  \(=45-30.15\)
  \(=$14.85\)

 

 \(\text{Percentage Discount}\) \(= \dfrac{\text{Discount}}{\text{Cost price}}\times 100\text{%}\)
  \(=\dfrac{14.85}{45}\times 100\text{%}\)
  \(=33\text{%}\)

Percentages, SM-Bank 088

Calculate the percentage profit on an item having a cost price of $25 and a sale price of $46.25. (2 marks)

Show Answers Only

\(85\text{%}\)

Show Worked Solution
 \(\text{Profit}\) \(=\text{Sale Price}-\text{Cost Price}\)
  \(=46.25-25\)
  \(=$21.25\)

 

 \(\text{Percentage Profit}\) \(= \dfrac{\text{Profit}}{\text{Cost price}}\times 100\text{%}\)
  \(=\dfrac{21.25}{25}\times 100\text{%}\)
  \(=85\text{%}\)

Percentages, SM-Bank 087

Iggy bought an e-bike for $3500 in 2022 and sold it in 2023 for $2450 to pay for an overseas holiday.

  1. Calculate the loss that Iggy made.  (1 mark)

  2. Calculate the percentage loss on the original price.  (2 marks)

Show Answers Only

a.    \($1050\)

b.    \(30\%\)

Show Worked Solution
a.    \(\text{Loss}\) \(=3500-2450=$1050\)

 

b.    \(\text{Percentage Loss}\) \(= \dfrac{\text{loss}}{\text{original price}}\times 100\text{%}\)
  \(=\dfrac{1050}{3500}\times 100\text{%}\)
  \(=30\%\)

Percentages, SM-Bank 086

Janice bakes cupcakes for the local market. The ingredients she uses in each of the cupcakes cost $1.90.

Last weekend she sold the cupcakes for $3.99 each.

  1. What was Janice's profit per cupcake?  (1 mark)

  2. Calculate Janice's percentage profit per cupcake based on the cost of the ingredients.  (2 marks)

Show Answers Only

a.    \($2.09\ \text{per cupcake}\)

b.    \(110\%\)

Show Worked Solution
a.    \(\text{Profit}\) \(=3.99-1.90\)
  \(=$2.09\)

 

b.    \(\text{Percentage Profit}\) \(= \dfrac{\text{Profit}}{\text{Cost of ingredients}}\times 100\%\)
  \(=\dfrac{2.09}{1.90}\times 100\%\)
  \(=110\%\)

Percentages, SM-Bank 085

Mavis bought an original artwork as an investment. She paid \($15\ 400\) in 2018 and sold it in 2023 for \($24\ 024\).

  1. Calculate the profit that Mavis made on her artwork.  (1 mark)

  2. Calculate the percentage profit based on the original price.  (2 marks)

Show Answers Only

a.    \($8624\)

b.    \(56\text{%}\)

Show Worked Solution
a.    \(\text{Profit}\) \(=24\ 024-15\ 400\)
  \(=$8624\)

 

b.    \(\text{Percentage Profit}\) \(= \dfrac{\text{Profit}}{\text{Original price}}\times 100\text{%}\)
  \(=\dfrac{8624}{15\ 400}\times 100\text{%}\)
  \(=56\text{%}\)

Percentages, SM-Bank 084

Jeffrey bought a new car for \($35\ 000\) in 2021 and sold it in 2023 for \($21\ 000\).

  1. Calculate the loss that Jeffrey made.  (1 mark)

  2. Calculate the percentage loss on the new car price.  (2 marks)

Show Answers Only

a.    \($14\ 000\)

b.    \(40\%\)

Show Worked Solution

a.    \(\text{Loss}=35\ 000-21\ 000=$14\ 000\)
  

b.    \(\text{Percentage Loss}\) \(= \dfrac{\text{loss}}{\text{original price}}\times 100\%\)
  \(=\dfrac{14\ 000}{35\ 000}\times 100\%\)
  \(=40\%\)

Percentages, SM-Bank 083

Jock is a real estate agent who is paid 2.5% commission on all house sales.

Last month he sold houses to the value of \($2.5\ \text{million}\).

How much pay did Jock receive in the form of commission last month?  (2 marks)

Show Answers Only

\($62\ 500\)

Show Worked Solution
\(\text{Commission}\) \(= 2.5\text{%}\times 2\ 500\ 000\)
  \(=\dfrac{25}{1000}\times 2\ 500\ 000\)
  \(=$62\ 500\)

  
\(\therefore\ \text{Jock earned }$62\ 500\ \text{in commission.}\)

Percentages, SM-Bank 082

Louella is a boat broker who is paid 6.5% commission on all boat sales.

Last quarter she sold boats to the value of \($443\ 000\).

How much pay did Louella receive in the form of commission last quarter?  (2 marks)

Show Answers Only

\($28\ 795\)

Show Worked Solution
\(\text{Commission}\) \(= 6.5\text{%}\times 443\ 000\)
  \(=\dfrac{65}{1000}\times 443\ 000\)
  \(=$28\ 795\)

  
\(\therefore\ \text{Louella earned }$28\ 795\ \text{in commission.}\)

Percentages, SM-Bank 081

Hendry is a salesperson who is paid 5% commission on all sales.

Last month he sold goods to the value of  \($45\ 300\).

How much commission did Hendry receive last month?  (2 marks)

Show Answers Only

\($2265\)

Show Worked Solution
\(\text{Commission}\) \(= 5\%\times 45\ 300=\dfrac{5}{100}\times 45\ 300\)
  \(=$2265\)

  
\(\therefore\ \text{Hendry earned }$2265\ \text{in commission.}\)

Percentages, SM-Bank 080

The sale price of a parrot is $400.

The pet store gives Albert 25% off the sale price.

Albert has a pet store discount voucher that gives him a further $60 off the sale price.

What percentage of the original price does Albert pay for the parrot?  (2 marks)

Show Answers Only

\(60\text{%}\)

Show Worked Solution
\(\text{Sale Price}\) \(= \$400-(25\text{%}\times 400)\)
  \(=400-100\)
  \(=$300\)

  
\(\text{Purchase price}=300-60=$240\)

\(\text{Percentage of original price}\) \(=\dfrac{240}{400}\times 100\)
  \(=\dfrac{6}{10}\times 100\)
  \(=60\text{%}\)

Percentages, SM-Bank 079

A family ticket to Taronga Zoo in Sydney reduced in price from $90 to $73.80.

What is the percentage decrease in the price?  (2 marks)

Show Answers Only

\(18\text{%}\)

Show Worked Solution

\(\text{Price decrease}=90-73.80=$16.20\)

\(\text{Percentage decrease}\) \(= \dfrac{16.2}{90}\times 100\)
  \(=0.18\times 100\)
  \(=18\text{%}\)

 

Percentages, SM-Bank 078

A coffee shop increases the price of a caramel latte from $4.80 to $6.00.

What is the percentage increase in the price?  (2 marks)

Show Answers Only

\(25\text{%}\)

Show Worked Solution

\(\text{Price increase}=6-4.80=$1.20\)

\(\text{Percentage increase}\) \(= \dfrac{1.2}{4.8}\times 100\)
  \(=0.25\times 100\)
  \(=25\text{%}\)

 

Percentages, SM-Bank 077

A loaf of bread is on sale with a 15% discount.

In the last hour of trading, the bread is reduced a further 20% on the already discounted price.

What is the overall percentage discount on the bread?  (2 marks)

Show Answers Only

\(32\%\)

Show Worked Solution

\(\text{Strategy 1}\)

\(\text{Assume the bread costs }$1.00.\)

\(\text{Cost after }15\text{% discount}=$0.85\)

\(\text{Cost after further }20\text{% discount}\) \(= 0.85-(20\%\times 0.85)\)
  \(=0.85-0.17\)
  \(=$0.68\)

 
\(\therefore\ \text{Overall discount} =(1.00-0.68)\times 100 =32\text{%}\)
 

\(\text{Strategy 2}\)

\(\text{Overall discount}\) \(=1-(1\times 0.85\times 0.80)\)
  \(=1.00-0.68\)
  \(=0.32\)
  \(=32\%\)

Percentages, SM-Bank 076

A farmer sells a box of oranges to a supermarket with a 15% markup.

The supermarket then adds a further 20% on the already increased price.

What is the overall percentage markup on the box of oranges?  (2 marks)

Show Answers Only

\(38\%\)

Show Worked Solution

\(\text{Strategy 1}\)

\(\text{Assume the box of oranges costs }$1.00.\)

\(\text{Cost after }15\text{% markup}=$1.15\)

\(\text{Cost after further }20\text{% increase}\) \(= 1.15+(20\%\times 1.15)\)
  \(=1.15+0.23=$1.38\)

 
\(\therefore\ \text{Overall markup} =(1.38-1.00)\times 100 =38\%\)
 

\(\text{Strategy 2}\)

\(\text{Overall markup}\) \(=(1\times 1.15\times 1.20)-1\)
  \(=1.38-1.00=0.38=38\%\)

Percentages, SM-Bank 075

A car dealer decreases the price of a car from $50 000 to $45 000.

What is the percentage decrease in the price?  (2 marks)

Show Answers Only

\(10\text{%}\)

Show Worked Solution

\(\text{Price decrease}= 50\ 000-45\ 000=$5\ 000\)

\(\therefore\ \text{Percentage Decrease}\) \(= \dfrac{5\ 000}{50\ 000}\times 100\)
  \(=0.10\times 100\)
  \(= 10\text{%}\)

Percentages, SM-Bank 074

Lucia is saving her money to buy a jet ski.

After 3 months, she had saved 40% of the cost of the jet ski.

After 5 months, she had saved another $1200 and now had 60% of the cost of the jet ski.

How much does the jet ski cost?  (2 marks)

Show Answers Only

\($6000\)

Show Worked Solution
\(60\%-40\%\) \(= $1200\)
\(\therefore 20\%\) \(= $1200\)
\(\therefore\ 1\%\) \(= $60\)

 

\(\therefore\ \text{The cost of the jet ski}\) \(= 100\times 60= $6000\)

Percentages, SM-Bank 071

Lancelot bought a new round table for $2810.50 inclusive of 10% GST.

What was the price of the round table before the GST was added?  (2 marks)

Show Answers Only

\($2555\)

Show Worked Solution

\(\text{Round table has had 10% added to the price.}\)

\(\therefore\ $2810.50\ \text{represents}\ 110\text{%}\ \text{of the original price}\)

\(\therefore\ \dfrac{110}{100}\ \times\ \text{Original price}\) \(=$2810.50\)
\(\therefore\ \text{Original price}\) \(=\dfrac{$2810.50\times 10}{11}\)
  \(=$2555\)

Percentages, SM-Bank 070

Mickey bought a plane ticket to London for $1716 inclusive of 10% GST.

What was the price of the ticket before the GST was added?  (2 marks)

Show Answers Only

\($1560\)

Show Worked Solution

\(\text{Plane ticket has had 10% added to the price.}\)

\(\therefore\ $1716\ \text{represents}\ 110\text{%}\ \text{of the original price}\)

\(\therefore\ \dfrac{110}{100}\ \times\ \text{Original price}\) \(=$1716\)
\(\therefore\ \text{Original price}\) \(=\dfrac{$1716\times 10}{11}\)
  \(=$1560\)

Percentages, SM-Bank 069

James purchased a pair of football boots for $358.05.

This price included 10% GST.

What was the price of the shoes before the GST was added?  (2 marks)

Show Answers Only

\($325.50\)

Show Worked Solution

\(\text{Football boots have had 10% added to the price.}\)

\(\therefore\ $358.05\ \text{represents}\ 110\text{%}\ \text{of the original price}\)

\(\therefore\ \dfrac{110}{100}\ \times\ \text{Original price}\) \(=$358.05\)
\(\therefore\ \text{Original price}\) \(=\dfrac{358.05\times 10}{11}\)
  \(=$325.50\)

Percentages, SM-Bank 068

Minerva purchased a book online and a discount of 35% was applied at checkout.

If Minerva paid $29.90 with the discount, what was the original price of the book.  (2 marks)

Show Answers Only

\($46\)

Show Worked Solution

\(\text{Book price discounted by 35%.}\)

\(\therefore\ $29.90\ \text{represents}\ \dfrac{65}{100}\ \text{of the original price}\)

\(\therefore\ \dfrac{65}{100}\ \times\ \text{Original price}\) \(=$29.90\)
\(\therefore\ \text{Original price}\) \(=\dfrac{29.90\times 100}{65}=$46\)