By BYJU'S Exam Prep

Updated on: September 25th, 2023

Ratio and proportion are crucial topics in the quantitative aptitude section of competitive exams, particularly the SSC exams. Typically, 4-5 questions in the SSC exams are based on this topic. Understanding the concepts of ratio and proportion is essential because they are the foundation for grasping other mathematical concepts. In simple terms, a fraction written as a:b represents a ratio, whereas a proportion indicates that two ratios are equal. Both a and b can be any two integers.

However, some candidates often get perplexed by the concepts of ratio and proportion. If you are one of them, fret not. As this blog aims to provide candidates with a clear understanding of ratio and proportion through comprehensive explanations, formulas, ratio and proportion questions for SSC Exams and much more.

## Ratio and Proportion

Fractions are a way of expressing a portion of a whole. They are used to represent ratios and proportions in mathematics. A ratio compares two quantities by dividing one by the other, and it can be written in the form of a fraction a:b. A proportion is a statement that two ratios are equal, which means that they can be expressed as a fraction with the same value.

## Definition of Ratio

A ratio is a way of comparing two quantum measurements by employing a division of the same.

A ratio is a comparison of two quantities obtained by dividing one by the other. If a and b are two values of the same type and units, and b is not equal to zero, the quotient a/b is known as the ratio between a and b. Ratios are expressed using the colon (:) sign. This means that the a/b ratio has no unit and can be written as a: b.

## Definition of Proportion

It is an equation applied to two ratios to know whether they are equal or not.

Proportion refers to the equality of two ratios. Two proportionate ratios are always equal. The sign (::) represents proportions and helps us solve for unknown quantities. In other words, a percentage is an equation or statement that demonstrates that two ratios or fractions are equivalent. Four non-zero numbers, a, b, c, and d, are said to be in proportion if a: b = c: d. Consider the two following ratios: 3: 5 and 15: 25. In this scenario, 3:5 is represented as 3:5 = 3/5 = 0.6, and 15:25 is written as 15/25 = 3/5 = 0.6. We can argue that both ratios are proportionate since they are equal.

## Ratio and Proportion Formula

The formula for Ratio and Proportion is provided below:

Ratio

• a: b ⇒ a/b

Where a and b are any two quantities and “a” is called the antecedent (first term), and “b” is called the consequent (second term)

Proportion

• a/b = c/d or  a : b :: c : d

In proportion, the two ratios are a:b & c:d. The two terms ‘b’ and ‘c’ are called ‘means or mean term,’ whereas the terms ‘a’ and ‘d’ are known as ‘extremes or extreme terms.’

## Types of Proportion

There are different types of Proportions that are listed and described below:

Direct Proportion: The term direct proportion refers to the direct link between two quantities. When there is a rise in one quantity then the other one rises as well and vice versa. As a result, a direct proportion is written as y ∝ x. For example, increasing the speed of an automobile causes it to travel more distance in a given amount of time.

Inverse Proportion: Inverse proportion explains the relationship between two quantities in which one increases while the other falls and vice versa. As a result, an inverse proportion is expressed as y ∝ 1/x. For example, when a vehicle’s speed increases, it will travel a constant distance in less time.

## Difference between Ratio and Proportion

To understand the concept of Ratio and Proportion a little better, candidates can go through the difference between these two provided below:

 Proportion Ratio The proportion is used to express the relation between two ratios The ratio is used to compare the size of two things with the same unit It is expressed using the double colon (::) or equal to the symbol (=) It is expressed using a colon (:), slash (/) It is an equation It is an expression The keyword to identify proportion in a problem is “out of” The keyword to identify the ratio in a problem is “to every”

## Ratio and Proportion Questions with Solutions PDF

We have provided the most straightforward, easy-to-understand, and effective tips and tactics for solving ratio and proportion questions. Below we are going to provide you all with the Ratio and Proportion Questions with solutions PDF in order to make your SSC exam preparation more fruitful.

## Importance of SSC Ratio and Proportion Questions

SSC Ratio and Proportion Questions are of great relevance in the SSC Exams 2023 as:

• Competitive exams such as the SSC and all of its versions assess candidates’ numeric aptitude because demonstrating it allows exam makers to evaluate the taker’s fit for the profile. As a result, it is critical for students to be well-prepared in areas such as ratio and proportion.
• Ratio and proportion, unitary technique, fraction and percentage are fundamentals that serve as the foundation for more complex commercial mathematics topics covered in the SSC exam.
• Because ratio and proportion as a topic is strongly related to %, being competent in addressing its problems also helps applicants with percentage questions. This works in students’ favour because percentages are an important topic covered in the quantitative component of the SSC exam.
• Finally, studying ratio and proportion assists with preparation for other competitive government exams because this topic is covered in all of them.

## Ratio and Proportion Questions for SSC CGL

The topics of ratio and proportion hold great significance in the quantitative aptitude section of competitive exams like SSC CGL. Based on the SSC CGL Previous Year Papers, it has been observed that 4-5 questions are generally based on this topic. Therefore, it is crucial to prepare for these questions thoroughly. To help candidates prepare better, we have provided some important ratio and proportion questions that are frequently asked in SSC CGL.

1. Three numbers are in the ratio 3 : 5 : 11. If the sum of the first and the third is greater than the second by 333. The sum of three numbers is :

A. 741
B. 703
C. 1197
D. None of these

2. Rs 13450 are to be distributed between B and A such that B gets Rs 3400 less than A. The ratio of the amount received by A to that received by B is

A. 296 : 117
B. 7 : 3
C. 337 : 201
D. 199 : 105

3. The fourth proportional to 0.15, 0.27 and 16 is

A. 22.6
B. 33.7
C. 25.5
D. 28.8

4. Which of the following is the smallest fraction

A. 19/27
B. 7/13
C. 11/15
D. 12/23

5. A company employs experts, amateurs and novices in the proportion 2 : 7 : 11 and the wages of an expert, an amateur and a novice are in the ratio 7 : 4 : 2. When 33 novices are employed, the total monthly remuneration of all amounts to ₹ 1881600. Find the monthly remuneration of a person in each category of employees.

A. ₹ 63000, ₹ 36000, ₹ 18000
B. ₹ 68600, ₹ 39200, ₹ 19600
C. ₹ 66500, ₹ 38000, ₹ 19000
D. ₹ 67900, ₹ 38800, ₹ 19400

6. A person divided a certain sum between his three sons in the ratio 1 : 3 : 5. Had he divided the sum in the ratio  the son, who got the least share earlier, would have got ₹1456 more. The sum (in ₹) was:

A. 2691
B. 2961
C. 2916
D. 2196

7. A man plays 100 games with the cards. He gets Rs. 5 if he wins and pays Rs. 2 if he loses. If he wins Rs. 3 on the whole in how many games did he win?

A. 25
B. 28
C. 29
D. 32

8. The marks of three students A, B and C are in the ratio 10:12:15. If the maximum marks of the paper are 90, then the maximum marks of B can be in the range:

A. 70 – 80
B. 80 – 90
C. 20 – 30
D. 40 – 50

9. 4 years back, the age of Garvit was three times that of Yuvansh, but one year back the age of Garvit was two times that of Yuvansh, what is the age difference between their present ages?

A. 7 years
B. 13 years
C. 11 years
D. 6 years

10. A purse has Rs. 80 in the form of Rs. 2, Rs. 1, 50 Paise and 10 Paise coins in the ratio of 2:3:5:5, find the total number of coins.

A. 105 coins
B. 120 coins
C. 135 coins
D. 150 coins

## Important Ratio and Proportion Questions for SSC CHSL

Ratio and Proportion questions are an important component of the SSC CHSL exam as well. There are approximately 3-4 questions asked in the tier 1 examination and now that Maths is an integral part of the SSC CHSL tier 2 exam, this chapter has an additional weightage. Important Ratio and Proportion Questions for SSC CHSL are given below:

1.If (x + y):(x – y) = 11:1, find value of (5x + 3y)/(x – 2y).

A. 45/4
B. 4/45
C. -45/4
D. -4/45

2.A bag has Rs 34.2 in the form of 1-rupee, 50-paise and 10-paise coins in the ratio of 3:5:2. Find the number of 50-paise coins.

A. 30
B. 12
C. 18
D. 6

3.P started a business by investing Rs.35000 and Q joined him after one year with an amount of Rs.21000. After two years from the starting of the business, they earned a profit of Rs.26000. What will be the P’s share (in Rs.) in the profit?

A. 15000
B. 18000
C. 20000
D. 16000

4.Mohit and Anshu invested some money in a business in the ratio 8: 15 respectively. After 9 months Mohit withdraws his capital. If they receive profits in the ratio 4 : 5, then for how many months did Anshu invest in the business?

A. 4
B. 5
C. 8
D. 6

5.The ratio of two numbers is 2 : 3. If the sum of both the numbers is 75, then what is the larger number among both the numbers?

A. 45
B. 30
C. 50
D. 48

6.If 4P = 7Q = 21R, then what is P : Q : R?

A. 5 : 3 : 4
B. 21 : 12 : 4
C. 3 : 5 : 15
D. 15 : 5 : 3

7.The ratio of two numbers is 7 : 11. If both numbers are increased by 10, the ratio becomes 9 : 13. What is the sum of the two numbers?

A. 90
B. 32
C. 48
D. 160

8.If 5A = 3B, then what is the value of (A + B)/B?

A. 8/3
B. 8/5
C. 5/8
D. 5/3

9.The ratio of two numbers is 3:5. If both numbers are increased by 8, the ratio becomes 13:19. What is the sum of the two numbers?

A. 32
B. 48
C. 40
D. 72

10.The ratio of the speed of A, B and C is 2 : 3 : 6 respectively. What is the ratio of the time taken by A, B and C respectively to cover the same distance?

A. 2 : 3 : 6
B. 6 : 3 : 2
C. 3 : 2 : 1
D. 1 : 2 : 3

## Tips and Tricks to Solve SSC Ratio & Proportion Questions

Many methods and ideas for ratio and proportion questions can be discovered in books and easily taught. These methods and suggestions assist students in solving these problems, which are a component of competitive examinations such as the SSC, in a lot more enhanced manner and achieving speedier outcomes.

• Many students are perplexed when they see a ratio and proportion separated by fractions rather than colons. Fractions, like a colon, are used to determine whether the ratios are equal or proportional.
• Practice popular mathematics strategies like visualization to better understand the fundamentals of ratio and proportion.
• Individual values have the same denominator value for proportions with more than two ratio components.

## Best Books for SSC Ratio & Proportion Questions

As noted in the preceding section, ratio and percentage are significant components of the SSC CGL syllabus and SSC CHSL syllabus. As a result, it is critical to prepare thoroughly for this section. Here are some of the best books on ratio and proportion:

 Books Authors/Publishers Quantitative Aptitude for Competitive Exams RS Aggarwal Fast Track Objective Arithmetic Rajesh Verma Quantitative Aptitude for All Competitive Exams Abhijit Guha Objective Arithmetic S. Chand Publishing

In conclusion, candidates must comprehend with SSC Ratio and Proportion Questions to fetch maximum marks from this topic. If you are facing any difficulties, you should consider enrolling in SSC online coaching and attempting SSC mock tests to work on your weak areas.

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