Worked out examples

Examples on ratio definitions:

The ratio between Rs.50 and Rs.10 is 50 : 10 = 50/10 = 5 / 1 = 5 : 1
The ratio between 5 kg and 15 kg is 5 : 15 = 5 / 15 = 1 / 3 = 1 : 3
The ratio between Rs.1 and 5 kg is not possible, since they are of different units.

Examples on important property:

5 / 15 = (5 × 8) / (15 × 8) shows that 5 : 15 is equal to 40 : 120
3 / 7 = [3 / 5] / [7 / 5] shows that 3 : 7 is equal to 3 / 5 : 7 / 5

Examples on ratio in simplest form:

Find out the ratio of cherries to the grapes and what is the simplest form of that ratio ?

Solution:

Given,
Number of cherries = 4
Number of grapes = 2
Required ratio =

Simplest form of ratio =

Example on compound ratio:

Find the compound ratio of following figures ?

Solution:

There are 3 blue balls and 4 red balls are present in first image. So the retio of blue balls and 3 red balls are present in second image. Therefore the ratio of blue balls to the red balls in second image is

.
Compound ratio =

Example on compound ratio:

If P : Q = 8 : 6 and Q : R = 6 : 5 then P : Q : R = 8 : 6 : 5

Example on direct proportion:

If the cost of one book is Rs.6 then the cost of 10 books is Rs.60 and 15 books cost is Rs.90....

So, if number of books are increased automatically cost also increases i.e, the number of books is in direct proportion with the cost of books.

(Ratio of number of books) : : (Ratio of cost of books)

Example on indirect proportion:

Time taken to finish a work is inversely proportional to number of persons at work (More persons, less is the time taken to finish a work)

(Ratio of men) : : (Inverse ratio of time taken)