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Solved problems for the chapter:

Ratio and proportion

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Proportion and percentage change

1. Proportion

1.1. Direct proportion

1.2. Inverse proportion

2. Change

2.1. Relative change

2.2. Percentage Change

2.2.1. Relationship between relative change and percentage change

3. Forum

View the theory »

Solving linear equations and systems of equations for KS4

1. Solving Equations

1.1. Special examples of solutions of equations

1.1.1. The solution is all real numbers

1.1.2. The equation has no solutions

1.2. Equivalent or equivalent equation

1.3. Solving higher degree equations and splitting equations

2. Solving the system of two linear equations

2.1. Substitution method

2.2. Elimination Method

3. Solving the system of three linear equations

3.1. Elimination method

4. Forum

↓ Show theory [2] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:ratio_and_proportion/5305/

Example 1.

If it takes three workers 15 days to complete a task by working 10 hours a day, how many workers would have to work 5 hours a day to do the same work in 10 days.

Example 2.

If 5 workers complete a work in 10 days by working 8 hours a day, how long would it take 8 workers to complete the same work if they worked 10 hours a day?

Simplify the ratio:

Write the expression as a ratio.

Write as a ratio.

Mark had a glass of juice and water mixed in a ratio of , and George . Who had a thinner mixture?

Complete the table and find out what the ratios are.

Mass (kg)
Value (£)
Number of workers
Time of work performed (h)

10.

In the zoo they have 21 monkeys, 7 elephants, 12 pelicans and some giraffes. How many giraffes must there be for the ratio of monkeys to elephants to be the same as the ratio of pelicans to giraffes?

11.

Simplify the given ratios:

12.

Calculate the unknown term from the ratio !

13.

There are boys and girls in the 9th grade. What is the simplified ratio of boys to girls in 9th grade?

14.

At the Olympic Games, marathoner run is the longest run, which measures 42 km. One of the runners ran 16 km at one point. Write down and simplify the following relations:

Ratio of the distance covered in relation to the entire marathon.
The ratio of the remaining distance to the entire marathon.
Ratio of traveled distance to remaining distance.

15.

They want to plant apple and pear trees in the new orchard in the ratio of 7:5. How many apple trees and how many pears should there be if they want to have 40 more apple trees than pears in the orchard?

16.

24 students applied for the mathematics competition. How many boys and how many girls were there if the ratio of boys to girls was 3:5?

17.

Calculate the unknown term from the ratio !

18.

Mary would like to prepare litres of drink for her birthday. She read in the instructions that to prepare the drink she must mix syrup and water in the ratio How many dl of each of the ingredients does she need?

19.

Martha would like to prepare a drink. She found a bottle of syrup in the cupboard. In the instructions for preparing the drink, it is written that the syrup and water should be mixed in a ratio of . How much water should add to the syrup?

20.

One half of two fifths of a number is equal to three fifths of another number. What is the ratio of the two numbers?

21.

The length of the interactive whiteboard is 2.6 m. The width of the interactive whiteboard is 1.3 m. Write down the simplified ratio between the length and width of the interactive whiteboard.

22.

Calculate the unknown term of the proportion .

23.

Work on a construction site is completed by 10 workers in 20 hours. How long does it take 8 workers to do the same job?

24.

Calculate the unknown term of the proportion .

25.

Calculate the unknown term of the proportion .

26.

Fills the table if and are inversely proportional to quantity.

27.

Is the given ratio inverse? Justify the answer.

28.

The sum of the numbers in the ratio is equal to . What numbers are these?

29.

We have 6 boxes of kg of potatoes. Half of the potatoes will be transferred to kg bags and the other half to kg bags. How many large and small bags will we get?

30.

If there are eighteen children in a class, how many children would be in each group if they were divided into two, three or six groups? Draw a graph of the ratio between the number of groups and the number of children in each group.

31.

The ratio between the number of adults and the number of children at the concert was . There were children. A ticket for an adult was twice as expensive as a ticket for a child. Proceeds from ticket sales amounted to . What was the price of an adult ticket?.

32.

Mac and Zainab share their pocket money in the ratio of . How much does Zainab get if they were given ?

Mass (kg)
Value (£)

Number of workers
Time of work performed (h)