Mensuration is the study of the measurement of geometrical figures and their parameters like volume, area, height, perimeter, etc. The subject deals with the length, volume, area, perimeter, the total surface area of different two-dimensional and three-dimensional geometrical shapes. These shapes exist on plane surfaces. The two-dimensional shapes have dimensions of length and breadth only. Whereas, three-dimensional shapes deal with the dimensions like length, breadth, and height or depth. 

What is the percentage?

The percentage is a ratio represents as a fraction of 100. It is a number with no unit of measurement and is generally, denoted by the mathematical symbol (%). The percentage value is calculated by multiplying the given ratio of numbers by 100.

Example: If we have to calculate what percent is 50 balls out of 1000 balls in the basket we will first have to compute a ratio and then multiply it by 100 to gain a percentage value.

Solution:

= 50/1000

= 0.05

0.05 is the ratio of the numeric value. Now, multiplying the ratio by 100

= 0.05 x 100

= 5%

What percentage of 90 is 120?

Solution:

Let us consider a number to be x.

By the standard method of percentage calculation.

= x % of 90 = 120

= x/100 x 90 = 120

= 90x = 12000

= x = 12000/90

= x = 133.33%

Therefore, 133.33% is the percentage of 120 of 90.

Sample problems

Problem 1: What is 35% of 80?

Solution:

By the question,

= 35% of 80

= 35/100 x 80

= 0.35 x 80

= 28

Problem 2: What is 25% of 80?

Solution:

By the question,

= 25% of 80

= 25/100 x 80

= 0.25 x 80

= 20

Problem 3: What is the percentage of 90 of 120?

Solution:

By the question,

= x% of 120 = 90

= x/100 x 120 = 90

= x = 90 x 100/120

= x = 75

Problem 4: What is 30% of 60?

Solution:

By the question,

= 30% of 60

= 30/100 x 60

= 0.30 x 60

= 18