CSEET Quantitative aptitude - Percentage

Percentage

The term "percentage" was adapted from the Latin word "per centum", which means "by the hundred". Percentages are fractions with 100 as the denominator. In other words, it is the relation between part and whole where the value of "whole" is always taken as 100.

What is the Percentage?

The percentage is a fraction or a ratio in which the value of the whole (denominator) is always 100. For example, if Sam scored 30% marks in his math test, it means that he scored 30 marks out of 100. It is written as 30/100 in the fraction form and 30:100 in terms of ratio. Here "%" is the symbol of percentage and is read as "percent" or "percentage". This percent symbol can always be replaced with "divided by 100" to convert it into a fraction or decimal equivalent.

Examples of Percentage

10% = 10/100 ( = 1/10 (or) 0.1)

25% = 25/100 ( = 1/4 (or) 0.25)

12.5% = 12.5/100 ( = 1/8 (or) 0.125)

50% = 50/100 ( = 1/2 (or) 0.5)

Calculating Percentage

Calculating percentage means finding the share out of the whole, in terms of 100. There are two ways to calculate percentage:

By changing the denominator of the fraction to 100: In this method, we just find the equivalent fraction of a given fraction such that the resultant denominator is 100. Then the numerator itself is the percentage. For example:

4/25 = 4/25 × 4/4 = 16/100 = 16%

By using the unitary method: In this method, we just multiply the fraction by 100 to get the percentage. For example, the percentage that corresponds to the fraction 4/25 is:

4/25 × 100 = 400/25 = 16%

It should be noted that the first method for calculating the percentage is not suggested in situations where the denominator is not a factor of 100. In such cases, we use the unitary method.

Percentage Formula

The percentage formula is used to find the share of a whole in terms of 100. Using this formula, you can represent a number as a fraction of 100. If you observe carefully, all three ways to get the percentage shown above can be easily calculated by using the formula given below:

Percentage = (Value/Total Value)×100

Example: In a class of 40 children, 10 are girls. Then what is the percentage of girls?

Solution: Here, the number of girls = 10.

The total number of children = 40.

By the percentage formula,

the percentage of girls = 10/40 × 100 = 25%.

Percentage Increase

Percentage increase refers to the percentage change in the value when it is increased over a period of time. For example, population increase, increase in the number of bacteria on a surface, etc. Percentage increase can be calculated by using the following formula:

Percentage Increase = (Increased Value-Original value)/Original value × 100

Example: The cost of a jacket is increased from $100 to $150. Then by what percentage the price is increased?

Solution: Percentage increase = (150 - 100) / 100 × 100 = 50%.

Percentage Decrease

Percentage decrease refers to the percentage change in the value when it is decreased over a period of time. For example, decrease in the level of rainfall, decrease in the number of Covid patients, etc. Percentage decrease can be calculated by using the following formula:

Percentage Decrease= (Original value-Decreased Value)/Original Value × 100

Example: The amount of rainfall has decreased from 127 mm to 103 mm. Then what is the corresponding percentage decrease?

Solution: Percentage decrease = (127 - 103) / 127 × 100 = 18.9% (Approximately).