11+ Maths Solved Topic Wise Questions

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=(4×12)⁄6

x=8

6 people can finish the same job in 8 days.