Comparison of Ratios in Mathematics

In order to compare quantities as a ratio, we would need to learn arranging the ratios.  The concept of ratio, proportion and variation is quite a crucial concept when it comes to competitive exams like JEE. Questions from these topics are frequently asked in the JEE examinations. In addition to the quantitative aptitude, comparison of ratios is also equally important for data interpretation questions. In data interpretation, comparing ratio and the change in ratio are a regular topic. In this article, we will learn the comparison of two ratios and how it is done in the simplest way.

(Image to be added soon)

How to Compare Ratios?

For the purpose of comparing two ratios, we will have to follow the below-mentioned:

Step I: Make the 2nd of both the ratios equal.

For this, identify the LCM (least common multiple) of the 2nd terms (denominator) of the ratios. Then, divide the LCM by the 2nd term of each ratio. Now, multiply the denominator as well as the numerator of each ratio by the quotient.

Step II: Compare the 1st terms (numerators) of the new ratios.

Solved Examples on Comparison of Ratios 

Example: Which of the following ratios is greater? 

Compare the ratios of the given quantities 1:5 and 7:4

Solution:

LCM of the 2nd terms, i.e., 5 and 4 = 20

Now, dividing the LCM by the 2nd term of each ratio, we get 20 ÷ 5 = 4, and 20 ÷ 4 = 5

Therefore,

(1 × 4) (5 × 4) = 4 and 20

(7 × 5) (4 × 5) = 35 and 20

Since, 35 > 4 and 20 = 20

Hence the ratio 7:4 is greater than the ratio 1: 5 as per the ratio comparison rules.

Determining The Gap Between 3 or More Than 3 Quantities

Comparing quantities as a ratio is quite useful when we need to compare 3 or more quantities. Suppose that you are given a ratio relationship between the salaries of two employees A and B. Furthermore, there is yet another relationship between B and C. Then by combining the two ratios provided to you, you can easily present a single ratio between A, B, and C. This ratio will deliver you the relationship between A and B. Additionally, the questions and problems about the comparison of salaries of two or more individuals is quite common in competitive exams. That said, let’s take a look at an example one like below:

Example

Ratio of A’s salary given to B’s salary is 2:3. While the ratio of B’s salary to C’s salary is 4:5. Find out the ratio of A’s salary to C’s salary?

This question is actually an exemplary problem of the type of question regularly asked in a competitive exam. It can be easily solved using two methods.

Method 1: Conventional Method to Solve the Question

Let’s get started with the two values of B, as they are common values provided in the ratio. Hence, 3 and 4 are those two values. We need to take the LCM of these values. The LCM of the given values i.e. 3 and 4 will be 12. Now, convert B’s value in each ratio to 12.

Therefore, ratio 1 = 8/12 and the ratio 2 = 12/15

Hence, A : B : C = 8 : 12 : 15.

So, if it was given that A’s salary was 100 then we can find out that C’s salary was Rs. 450.

Method 2: Shortcut Method

You can find the 1st method of the LCM to be a little tiresome and tricky in case the values are very high and thus it can become difficult to form a bridge between the three quantities.

The ratios given in the question are:

A: B = 2: 3

B: C = 4: 5

Then to calculate the ratio of A and C, we simply need to multiply the 1st digits with one another and 2nd digits with one another. So, A: C = 2 x 4 : 3 x 5 = 8 : 15.