# Solve Real Life Proportion Questions

In this worksheet, students will solve real life proportion problems with two or more variables using the methods of applying and manipulating the information provided in the question.

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:

### QUESTION 1 of 10

One of the most common uses for proportion in maths is to solve real-world problems.

In these, we will be given a fact and asked to use it to find another amount.

Let's look at this in action now.

e.g. If 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 we already know.

2 hours = 10 m2

Step 2: Find the Highest Common Factor (HCF) of the proportion we already know and the element we are trying to find.

2 hours = 10 m2

1 hour = 5 m2

Note: Whatever we do to one side, we need do to the other which, in this case, this is ÷ 2.

Step 3: Use the information we have found to answer the question.

1 hour = 5 m2

5 hours = 25 m2

So it takes 5 hours to mow 25 m2 of grass, based on the current proportion provided.

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

This one is a little more complicated as we have three variables present.

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

4 people = 3 hours = 60 cars

The key step to apply here is that we can only change two of the three quantities at once.

We need to keep testing and making changes to two elements at a time, until we have the cars as 80 and the people as 2.

Change 1:

4 people = 3 hours = 60 cars    ÷ Both by 3

So 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    × Both by 4

So 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    ÷ People by 2, doubles the hours required

So if half as many people are cleaning the same amount of cars, it will take twice as long:

2 people = 8 hours = 80 cars

So based on the proportion given, it will take 2 people 8 hours to clean 80 cars.

In this activity, we will solve real life proportion problems with two or more variables using the methods shown above of applying and manipulating the information provided in the question.

A car can travel 300 miles on 40 litres of petrol.

How far can it travel on 60 litres of petrol?

150 miles

450 miles

300 miles

A man can cycle 30 miles in 4.5 hours.

How long will if take him to travel 100 miles?

150 miles

450 miles

300 miles

50 kg of potatoes will last a family of four people for 10 weeks.

How many weeks will 65 kg last?

150 miles

450 miles

300 miles

If 50 kg of potatoes will last the family for 10 weeks, what weight of potatoes will they need for 15 weeks?

150 miles

450 miles

300 miles

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

If the hole needs to be 10 m deep, match each time taken on the left below with the correct number of people on the right.

## Column B

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

60 phones can be repaired at a shop in 1.5 hours.

Based on this information, match the number of phones on the left with the correct length of time it takes to repair them on the right.

## Column B

40 phones
30 minutes
20 phones
1 hour
70 phones
3 hours and 45 minutes
10 phones
15 minutes

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

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

20 minutes

2 hours

3 hours

10 people take 2 hours to make 30 cakes.

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

20 minutes

2 hours

3 hours

One gardener cuts 40 m2 of grass in 1 hour.

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

20 minutes

2 hours

3 hours

4 people can make a cabinet in 8 hours.

How long will it take 2 people to make 3 cabinets?

20 minutes

2 hours

3 hours

• Question 1

A car can travel 300 miles on 40 litres of petrol.

How far can it travel on 60 litres of petrol?

450 miles
EDDIE SAYS
Step 1: Write out the proportion we already know. 300 miles = 40 litres Step 2: Find the Highest Common Factor (HCF) of the proportion we already know and the element we are trying to find. The HCF of 40 and 60 is 20: 40 litres = 300 miles ÷ 2 20 litres = 150 miles Step 3: Use the information we have found to answer the question. 20 litres = 150 miles × 3 60 litres = 450 miles So a car can travel 450 miles using 60 litres of petrol, based on the current proportion provided.
• Question 2

A man can cycle 30 miles in 4.5 hours.

How long will if take him to travel 100 miles?

EDDIE SAYS
Step 1: Write out the proportion we already know: 30 miles = 4.5 hours Step 2: Find and apply the Highest Common Factor (HCF): The HCF of 30 and 100 is 10 so... 30 miles = 4.5 hours ÷ 3 10 miles = 1.5 hours Step 3: Answer the question: 10 miles = 1.5 hours × 10 100 miles = 15 hours So it will take this man 15 hours to cycle a distance of 100 miles, based on the current proportion provided.
• Question 3

50 kg of potatoes will last a family of four people for 10 weeks.

How many weeks will 65 kg last?

EDDIE SAYS
Step 1: 50 kg = 10 weeks Step 2: The HCF of 50 and 65 is 5 so... 50 kg = 10 weeks ÷ 10 5 kg = 1 week Step 3: 5 kg = 1 week × 13 (65 ÷ 5) 65 kg = 13 weeks So 65 kg of potatoes will last this family of four for 13 weeks, based on the current proportion provided.
• Question 4

If 50 kg of potatoes will last the family for 10 weeks, what weight of potatoes will they need for 15 weeks?

EDDIE SAYS
We know from the previous question that the family need 5 kg for one week, so: 5 kg = 1 week 5 kg = 1 week × 15 75 kg = 15 weeks So 75 kg of potatoes will last this family of four for 15 weeks, based on the current proportion provided.
• Question 5

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

If the hole needs to be 10 m deep, match each time taken on the left below with the correct number of people on the right.

## 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 inverse proportion? So the more people who are digging, the less time it will take. We are already given a starting metric which we can apply to all the scenarios here: 40 people = 10 m = 1 hour / 60 mins We only need to manipulate the two metrics related to people and time to find our matches. 20 people = 10 m = 2 hours (half people, twice time) 10 people = 10 m = 4 hours (quarter people, 4 times the time) 80 people = 10 m = 30 minutes (double people, half time) 60 people = 10 m = 45 minutes (1.5 times people, 0.75 times time)
• Question 6

60 phones can be repaired at a shop in 1.5 hours.

Based on this information, match the number of phones on the left with the correct length of time it takes to repair them on the right.

## Column B

40 phones
1 hour
20 phones
30 minutes
70 phones
3 hours and 45 minutes
10 phones
15 minutes
EDDIE SAYS
All of these amounts are multiples of 10, so it makes sense to convert the proportion we have been given into this metric: 60 phones = 1.5 hours / 90 mins ÷ 6 10 phones = 15 mins Now we can apply this information to find the matches, one at a time. 40 phones = 15 × 4 = 60 mins / 1 hour 20 phones = 15 × 2 = 30 mins 70 phones = 15 × 7 = 225 mins / 3 hours and 45 mins 10 phones = simply 15 mins Were you able to match those successfully?
• Question 7

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

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

3 hours
EDDIE SAYS
We know that the number of phones is staying the same in both scenarios, so we can ignore this number for now. We also know that 3 people take 1 hour so we can write this equation: 3 people = 1 hour / 60 minutes The common mistake here is to divide the time by 3, because we divided the people by 3. Think carefully, will it really take one person, one third of the time? No, it will take them the inverse, which is three times the time: 1 hour × 3 = 3 hours
• Question 8

10 people take 2 hours to make 30 cakes.

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

EDDIE SAYS
This question is simpler than it looks if we apply some logic. If we were creating twice as many cakes, it would take the same number of people twice as long. Similarly, if we are using half the people to create twice the number of cakes, it will also take twice as long again. So we can find our answer by simply multiplying by 2 × 2: 2 hours × 4 = 8 hours
• Question 9

One gardener cuts 40 m2 of grass in 1 hour.

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

EDDIE SAYS
Always start by setting up the proportion that we know: 1 gardener = 40 m2 = 1 hour Then we need to change two of the three variables at the same time: 1 gardener = 40 m2 = 1 hour (double gardeners, halve time) 2 gardeners = 40 m2 = 0.5 hours 2 gardeners = 40 m2 = 0.5 hours (halve area, halve time) 2 gardeners = 20 m2 = 0.25 hour 2 gardeners = 20 m2 = 0.25 hour 2 gardeners = 60 m2 = 0.75 hour (triple area, triple time) So it will take 2 gardeners 0.75 hours to mow 60 m2 of grass, which is the equivalent of 45 minutes.
• Question 10

4 people can make a cabinet in 8 hours.

How long will it take 2 people to make 3 cabinets?

EDDIE SAYS
Again, we can solve this one using logic. Half the people will make a cabinet in double the time. Three times the number of cabinets to make will take the group three times as long. So we need to apply the sum × 2 × 3: 8 hours × 2 × 3 = 48 hours You can now solve real life proportion problems with two or more variables using the methods of applying and manipulating the information provided in the question - an essential skill for success in your GCSE exams!
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