The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Use Real-Life Proportion Questions

In this worksheet, students practise using proportion to solve real-world problems.

'Use Real-Life Proportion Questions' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Direct and Inverse Proportion

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

One of the uses for proportion is to solve real-world problems. In these, you are given a fact and asked to use it to find another amount.

 

Example 1: It takes 2 hours to cut 10 m2 of grass. How long does it take to cut 25 m2 of grass.

Step 1: Write out the proportion you know.

2 hours = 10 m2

Step 2: Find the Highest common factor of the thing you know (10m2) and the thing you are trying to find (25m2). For this question, it would be 5.

2 hours = 10 m2

1 hours = 5 m2

(Note: Whatever you do to one side, you do to the other)

Step 3: Use this to answer the question.

1 hours = 5 m2

5 hours = 25 m2

 

Example 2: 4 people take 3 hours to clean 60 cars. How long will it take 2 people to clean 80 cars?

This one is a bit more complicated

Our first step is to write out what we know as an equation.

4 people = 3 hours = 60 cars.

The key thing to know here is that we only change two of the three quantities at once, we have to keep playing until we have the cars as 80 and the people as 2.

Change 1:

4 people = 3 hours = 60 cars

If the same amount of people are cleaning one third of the cars, it will take one third of the time.

4 people = 1 hour = 20 cars.

Change 2:

4 people = 1 hour = 20 cars.

If the same amount of people are cleaning 4 times as many cars, it will take them 4 times as long.

4 people = 4 hours = 80 cars.

Change 3:

4 people = 4 hours = 80 cars.

If half as many people are cleaning the same amount of cars, it will take twice as long.

2 people = 8 hours = 80 cars.

A car can travel 300 miles on 40 Litres of fuel. How far can I travel on 60 L?

150 miles

450 miles

A man can cycle 30 miles in 4.5 hours. How long will if take to travel 100 miles?

150 miles

450 miles

50 kg of coal will last for 10 weeks.

How many weeks will 65 kg last?

50 kg f coal will last for 10 weeks.

How much coal will I need for 15 weeks?

40 people dig a hole 10 m deep in 1 hour.

 

If the hole needs to be 10 m deep, match the times and the number of people.

Column A

Column B

20 people
45 minutes
10 people
30 minutes
80 people
2 hours
60 people
4 hours

60 phones can be repaired in 1.5 hours.

 

Match the number of phones and how long it takes to repair them.

Column A

Column B

40 phones
105 minutes
20 phones
30 minutes
70 phones
15 minutes
10 phones
1 hour

In a mobile phone shop, 3 people sell 45 phones an hour.

 

How long will one person take to sell the same amount of phones?

20 minutes

3 hours

10 people take 2 hours to make 30 cakes

 

How long will it take 5 people to make 60 cakes?

20 minutes

3 hours

A gardener cuts 40 m2 of grass in 1 hour.

How long will it take 2 gardeners to cut 60m2 of grass?

 

(just put the number for your answer, don't worry about the units)

 

4 people can make a cabinet in 8 hours.

 

How long will it take 2 people to make 3 cabinets

 

(just put the number for your answer, don't worry about the units)

 

  • Question 1

A car can travel 300 miles on 40 Litres of fuel. How far can I travel on 60 L?

CORRECT ANSWER
450 miles
EDDIE SAYS
We first need to find the HCF of 40 and 60. This is 20 L 20L will allow me to go 150 miles. 60L will allow me to go ...
  • Question 2

A man can cycle 30 miles in 4.5 hours. How long will if take to travel 100 miles?

CORRECT ANSWER
EDDIE SAYS
if 30 miles is 4.5 hours. 10 miles = 1.5 hours How can we use this to find 100 miles?
  • Question 3

50 kg of coal will last for 10 weeks.

How many weeks will 65 kg last?

CORRECT ANSWER
13
EDDIE SAYS
If 50kg lasts 10 weeks, 5 kg will last one week. Where do we go from there?
  • Question 4

50 kg f coal will last for 10 weeks.

How much coal will I need for 15 weeks?

CORRECT ANSWER
EDDIE SAYS
We need to find the HCF of 10 and 15. This is 5 weeks. We need 25 kg for 5 weeks. How do we use this to find 15 weeks?
  • Question 5

40 people dig a hole 10 m deep in 1 hour.

 

If the hole needs to be 10 m deep, match the times and the number of people.

CORRECT ANSWER

Column A

Column B

20 people
2 hours
10 people
4 hours
80 people
30 minutes
60 people
45 minutes
EDDIE SAYS
Did you notice that this is an inverse proportion? The more people, the less time it will take.
  • Question 6

60 phones can be repaired in 1.5 hours.

 

Match the number of phones and how long it takes to repair them.

CORRECT ANSWER

Column A

Column B

40 phones
1 hour
20 phones
30 minutes
70 phones
105 minutes
10 phones
15 minutes
EDDIE SAYS
With these, its always easier to find the smallest one first. If 60 phones take 1.5 hours, this is 60 phones in 90 minutes We can use this to find that 10 phones take 15 minutes. All the other can be found from this.
  • Question 7

In a mobile phone shop, 3 people sell 45 phones an hour.

 

How long will one person take to sell the same amount of phones?

CORRECT ANSWER
3 hours
EDDIE SAYS
We know the number of phones is staying the same so we can ignore that for now. We know that 3 people take 1 hour. The common mistake here is to divide the time by 3 because you divided the people by 3. Think carefully here. Will it really take one person one third of the time?
  • Question 8

10 people take 2 hours to make 30 cakes

 

How long will it take 5 people to make 60 cakes?

CORRECT ANSWER
EDDIE SAYS
Twice as many cakes means twice as long Half the people working means twice as long. This can be simply done by multiplying the time by 4
  • Question 9

A gardener cuts 40 m2 of grass in 1 hour.

How long will it take 2 gardeners to cut 60m2 of grass?

 

(just put the number for your answer, don't worry about the units)

 

CORRECT ANSWER
0.75
45
EDDIE SAYS
Allways start by setting up the proportion that you know. 1 gardener = 40m2 = 1 hour Then we need to change two of the three at the same time 1 gardener = 40m2 = 1 hour 2 gardeners = 40m2 = 0.5 hours 2 gardeners = 40m2 = 0.5 hours 2 gardeners = 20m2 = 0.25 hour 2 gardeners = 20m2 = 0.25 hour 2 gardeners = 60m2 = 0.75 hour
  • Question 10

4 people can make a cabinet in 8 hours.

 

How long will it take 2 people to make 3 cabinets

 

(just put the number for your answer, don't worry about the units)

 

CORRECT ANSWER
48
EDDIE SAYS
You can do this logically Half the people will make a cabinet in double the time. Three times the cabinets will take three times as long. So all we have to do is double the time and then times it by three.
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Start your £1 trial today.
Subscribe from £10/month.