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Ratios and Proportions

Comparison of Ratios

The concept of ratio, variation, and proportion is a very important concept in the competitive exams. The questions from this topics are regularly asked in the exams. Along with the quantitative aptitude, this topic is also important for data interpretation questions. In data interpretation, the Ratio comparison and the change in ratio is a very common topic.

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Ratio Comparison

Whenever you are comparing two numbers, it becomes necessary to find out how many times is the one number greater than the other number. You can say that in other words, we need to express one number as a fraction of the other number. Usually, the ratio of a number x to a number y is defined as the quotient of the numbers x and y. The numbers used in the formation of the ratio are called terms of the ratio. The ratio is very often used to express as the percentages. To convert the ratio into a percentage we often multiply it by 100.

Ratio comparison

Comparing Percentage Values

Ratio comparison is used to compare which numbers are higher and to calculate the percentage of the number. You need to compare the two fractions than the ratio comparison is used. For example, you need to compare  \( \frac{163}{202} \)  and \( \frac{171}{231} \)

Now, in such cases just by estimating 10% ranges for the ratios you can clearly see that the first ratio given will be greater 80% and the second ratio given will be less than 80%. Because 10% of 163/202 will be 16.3/20 which is greater than 80 and 10% of 171/231 is 17.1/23.1 which is clearly less than 80%. Thus you can compare both the numbers easily and say that 163/202 will be greater.

So, you can see that if the given numbers to you are in the different 10% range of each other than both of them can be easily comparable. But there can problems in comparison when both the given ratio are in the same 10% range. For example, 163/201 and 171/211 are the given ratios and the range for both the numbers fall in the same range i.e 80% and 90%. Then you need to compare them using 1% range. The first ratio is in the range of 81 and 82 while the second ratio is in the range of 80 and 81. The best way to go about this method is to master the rules of percentage.

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Finding the Gap Between 3 or more Quantities

Ratio comparison is very useful when you are required to compare 3 or more quantities. Let’s assume that you are given a ratio relationship between the salaries of two individuals P and Q. In addition to this, there is another relationship between Q and R. Then by combining the two ratios given to you, you can easily come up with a single ratio between P, Q, and R. This ratio will also provide you with the relationship between P and R. Also, the questions about the comparison of salaries of two or more people is a very common question in competitive exams. Let’s look into one.


The ratio of P’s salary to Q’s salary is 2:3. The ratio of Q’s salary to R’s salary is 4:5. What will be the ratio of P’s salary to R’s salary?

The above question is a classic example of the type of question asked in a competitive exam. It can be solved by two methods.

Method 1: The conventional method to solve the question.

Let’s start with the two values of Q, as they are common values given in the ratio. Thus 3 and 4 are those two values and take LCM of the values. The LCM will be 12. Now, convert Q’s value in each ratio to 12.

So, ratio 1 = 8/12 and the ratio 2 = 12/15
Thus, P : Q : R = 8 : 12 : 15. So, if it was given that P’s salary was 400 then we can find that R’s salary was Rs. 750.

Method 2: Shortcut method

In method 1 the LCM given to you can become tiresome if the values are very high and thus it can become difficult to create a bridge between the three quantities.

The ratios given in the question are:
P : Q = 2 : 3
Q : R = 4 : 5

Then to find the ratio of P and R multiply the first digits with one another and second digits with one another. So, P : R = 2 x 4 : 3 x 5 => 8 : 15.

Practice Questions

1. Raju and Sanjay had 35% and 45% rupees more than Ajay respectively. What is the ratio of Raju and Sanjay’s money?

A. 7:9             B. 27:29               C. 37:39              D. 27:39

The correct answer is C.

2. Two men earn a yearly salary in the ratio 10:13. If there spending is in the ratio of 4:5 and the man spending lesser of the two saves Rs. 6000 while the other one saves Rs. 8000, then find the salary of the person who is higher paid.

A. Rs. 12000             B. Rs. 14000             C. Rs. 13000              D. Rs. 11000

The correct answer is C.

3. If the ratio of the ages of Priya and Sunanda is 6:5 at present, and after fifteen years from now, the ratio will be changed to 9:8, then find the Priya’s current age.

A. 22 years             B. 30 years              C. 34 years                D. 38 years

The correct answer is B.

4. P, Q, and R played cricket. P’s runs are to Q’s runs and Q’s runs are to R’s runs at 3:2. All of them scored a total of 342 runs. How many runs did P make?

A. 140             B. 154              C. 168                D. 162

The correct answer is D.

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