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Ratio and Proportion Questions and Answers

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Question 25 - Sevenoaks School Year 7 Entrance Exam 2023

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Question 03 - Bancrofts School 11 Plus Maths Sample Entrance Paper 2023

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Learn about Proportions for the 11 Plus Exams

1. Proportions

Proportions show how two or more quantities are related to each other. Proportion rules are the ones that govern the relation how the amount that quantities change in relation to each other. 

There are two types of proportion, direct proportion and inverse proportion. When solving problems involving proportion it is important to know which type of proportion that we are dealing with, direct proportion or inverse proportion.

Direct Proportion:

Two quantities are in direct proportion when one increases the other also increases. 

For example, If John can bake five cookies in 1 hour, how many cookies can he bake in 12 hours?

Solution:

As the number of cookies increases, time taken to bake those cookies will also increase.

This is an example of direct proportion.

In 1 hour, 5 cookies can be baked.

Let ‘x’ be the number of cookies baked  in 12 hours

Fraction of time taken to bake cookies = 1⁄12

Fraction of number of cookies =5⁄x

Using direct proportion relation:

1⁄12=5⁄x

x=(12×5)⁄1

x=60

In 12  hours, 60 cookies can be baked.

Inverse Proportion:

Two quantities are in inverse proportion when one increases the other decreases and conversely, as one value decreases, so does the other value.  

For example, Four people can complete a job in 12 days. How many days will it take for 6 people to finish the same job?

Solution:

As the number of people increases, the number of days required to finish the job decreases.

This is an example of inverse proportion.

Let ‘x’ be the number of days required for 6 people to finish the job.

Fraction of number of people = 4⁄6

Fraction of number of days = 12⁄x

Using inverse proportion relation:

4⁄6=x⁄12

x=(12)⁄6

x=8

6 people can finish the same job in 8 days.

Quiz Questions
65. Proportions
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65. Proportions Worksheet

 

 

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  • Frequently Asked Questions
    What is a good score in 11+ Maths ?

    What counts as a "good" score will vary depending on the school you want to attend. The standardized 11 Plus test score average across the country is roughly 100. The highest average in some areas is 111. The lowest scores would often fall between 60 and 70, while the highest scores would normally fall between 130 and 140. To achieve excellent marks on 11+ Maths Exams, practice 11+ Maths topic-wise questions.

    How to prepare for the 11+ Maths exam?

    The best way to prepare for the 11+ Maths Exam is by practicing 11+ Maths topic-wise questions regularly.

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    Maths online subscriptions are “Non-Refundable“. No refunds can be issued for any reason. This is because of the nature of digital products.

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    As these are digital products, we advise parents to go through our Free Past Papers provided on our website and once decided they can buy subscriptions.

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    What kind of questions are asked in the 11 Plus Maths exam?

    The majority of the 11 Plus Maths questions are mathematical problem-solving, where pupils need to understand and apply mathematical concepts. With regular practice of 11+ Maths Topic-wise questions, you will pass the 11-plus Maths Exam with a high score.

    What do you need to know for the 11 Plus Maths exam?

    The children must master the following topics for the 11 plus exams

    • Number and place value.
    • Addition, subtraction, multiplication, and division.
    • Fractions, percentages, decimals.
    • Ratio and proportion.
    • Algebra.
    • Measurement.
    • Geometry (properties and position of shapes, coordinates)
    • Statistics.

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