Ratio and Percentage

Introduction

Mathematics is a fascinating subject. It is an ocean of concepts, formulae, methods, and theorems. One of the important concepts in the subject is ratio and percentage. The aforementioned concept is taught at a very tender age. However, it can be applied in various dimensions of life. The other important concept can be proportion, which is related to ratios.

A percentage is expressed through a ratio which describes a value as the hundredth part of the whole. Without the concepts of ratios, the calculation of percentages would be hindered. The outcome from the ratio and percentage concept can help in analyzing performances.

Ratio and Proportion

Ratio is expressing the relation of a commodity or entity with another commodity. It is expressed in fraction form. The ‘:’ sign is used to denote a ratio. It is mostly incorporated to ascertain which one is of greater value. It is also incorporated while calculating a percentage.

The syntax of expressing a ratio is as follows:

Value 1: Value 2

While the ratio is simple, the proportion is much more complicated. It shows the relationship between four commodities. Ratio and proportion concepts are interrelated. Moreover, two ratios for an equation while being set equal then that equation is called a proportion. Here also ‘:’ sign is used to denote a proportion.

Value 1: Value 2: Value 3: Value 4

If a proportion a:b:c:d exists then a/b = c/d. 

Also, a × d = b × c.

Examples

Example 1.

There are 5 bananas and 10 apples. What is the ratio of apples to bananas?

Solution.

Number of apples= 10

Number of bananas= 5

The ratio of apples to bananas= Number of apples/ Number of bananas

= 10/5= 2/1

= 2:1

Ans. The ratio of bananas to apples is 2:1.

Example 2.

A and B decide to divide 100 units amid themselves in the ratio 2:3. What is B’s share?

Solution.

Given ratio= A:B= 2:3

Total of ratio values= 2+3= 5

B’s share= (2/5) × 100= 40 units

Ans. B’s share out of 100 units is 40 units.

Example 3.

Find x in the given proportion, 3:2:6:x.

Solution.

Given proportion= 3:2:6:x

Therefore, 3/2 = 6/x

3(x) = 2 × 6

x = 12/3 = 4

Ans. The value of x in the given proportion is 4.

Example 4.

A and B decided to divide 1000 units among themselves. If B’s share is 200 units more than that of A. Find A’s share.

Solution.

Let’s assume A’s share to be x

Therefore, B’s share = x + 200

B’s share= 1000-x

Therefore, x+200 = 1000-x

• 2x = 800
• x= 400

Therefore, B’s share= 1000-400= 600 units

Ans. B’s share out of 1000 units is 600 units.

Percentage

Percentage is expressing the share of a particular value out of a hundred. The word ‘cent’ in percentage means a hundred. It is used in various phases and dimensions of life. Organizations use it to ascertain their financial performance over a given period. Moreover, schools calculate students’ percentages for keeping a track of their performance. Moreover, percentages can also be used to aid statistical data. The results in the form of a percentage can be easier to form illustrations for statistical reference.

Percentage formula= (share/ total share)×100

Examples

Example 1.

There are 10 bottles of water in a room. If 2 people drink 2 bottles of water. What is the percentage of empty bottles?

Solution.

Total number of bottles= 10

Number of bottles emptied= 2

Percentage of bottles emptied= (2/10) × 100= 20%

Ans. The percentage of empty bottles is 20%.

Example 2.

A shopkeeper buys 3 pencils and 2 pens for 5 units and 10 units respectively. He sold them for 10 units and 15 units respectively. What is the percentage of profit earned for each of the commodities?

Solution.

Purchase price for 3 pencils =  5 units

Purchase price for 2 pens= 10 units

Selling price of 3 pencils= 15 units

Selling price of 2 pencils= 20 units

Profit for pencils= (10-5) units= 5 units

Profit for pens= (15-10) units= 5 units

Percentage of profit earned for pencils= (profit/purchase price) × 100= (5/5)×100= 100%

Percentage of profit earned for pens= (profit/purchase price) × 100= (5/10)×100= 50%

Ans. The percentage of profit earned by a shopkeeper for pencils and pens is 100% and 50% respectively.

Conclusion

Ratio, percentage, and proportion are important concepts of mathematics. The aforementioned concepts of mathematics are immensely useful in our daily life. The ratio and percentage concept helps in the financial world. It helps in ascertaining the financial performance and position of a business enterprise.

The concept of proportion is a little complicated compared to ratio. However, it becomes easier once its features are understood properly. The percentage also serves as a record for future reference and decision-making. Moreover, ratio analysis is vital for deriving conclusions from an organization’s financial statement.