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In management entrance tests such as the CAT, XAT, and NMAT, ratio and proportion are extremely important. It is an important section of the Arithmetic chapter and one of the most fundamental and simple concepts to comprehend. It’s also relevant in other areas of these entrance tests, such as Data Interpretation.
One of the most basic principles in CAT is ratio and proportions. It’s just an expansion of high school math. This concept’s questions are frequently asked in connection with others, such as comparable triangles, mixtures, and claims. As a consequence, the principles of this topic are significant not only in their own right, but also in answering questions about other topics.
Ratio and Proportion
When comparing two quantities that are the same, the ratio is used. The ratio formula is denoted as a: b or ab for two digits, a and b. Two or more ratios are considered to be in proportion when they are equal. Fractions underpin the concepts of ratio and proportion. Ratio and proportion are the foundations for many other mathematical topics. Ratio and proportion can be used to solve a wide variety of daily issues, like comparing heights, weights, distances, and times, or adding ingredients to a recipe.
A ratio is a divisional comparison of two quantities, and proportion is the equality of two ratios. A ratio can be written in a variety of forms, including x:y or xy , and is frequently phrased as x is to y.
On the other hand, proportion is an equation that implies that two ratios are similar. A proportion is represented as x: y: z: w and read as x: y: z: w. xy = zw in this scenario, where w and y are not equal to 0.
Questions on ratios and proportions for the CAT exam
Solved examples of Ratio and Proportion CAT Questions
Example 1: Determine whether the ratios 6:8 and 24:32 are equal.
Solution: The ratios 6:8 and 24:32 are presented as a solution. 6:8 = 0.75, and 24:32 = 0.75. Both ratios are equal in this instance. As a conclusion, 6:8 and 24:32 are proportional.
Example 2: A class consists of 30 students. Students who prefer Math versus those who prefer Science exceed those who prefer Science by a factor of two. Calculate the number of students who prefer Math and those who prefer Science.
Solution: There are 30 students in total. Assume that the number of students who prefer Math is twice that of those who prefer Science. We can say 2x + 3x= 30, 5x = 30, and x = 6. The number of students who prefer Math = 2x = 2 6 = 12 and the number of students who prefer Science = 3x = 3 6 = 18 are obtained by substituting the value of x = 6.
As a result, 12 students like math and 18 students favour science.
Example 3: Reduce the stated ratio to 87:75.
Solution: GCF should be determined first to simplify the provided ratio.
GCF of 87 and 75, respectively, is 3. Furthermore, we get 2925 by dividing each term by 3, i.e. (87 ×3)/(75× 3)
In its simplest form, the ratio 87:75 is 29:25.
Average, Ratio, and Proportion CAT Preparation Tips
The section below contains several CAT average, ratio, and proportion preparation suggestions.
Must understand the fundamental concept as well as the formulas.
Make a list of formulas and study them daily.
After reading the question, try to comprehend it completely.
Understand the terminologies used in each topic.
Do some practice on the question from last year’s paper.
Give a mock test at least twice a week.
Some Key Points to Remember
When comparing the sizes of two things, ratio is employed, while proportion is employed to indicate the relationship between two rations.
Proportion is generally a mathematical problem.
Ratio can be defined as: and proportion can be represented as ::
Aspirants can recognize ratio questions by looking for the expression ‘to every’ in the questions, while proportion questions can be recognized by looking for the expression ‘out of’ in the questions.
Importance of Ratio and Proportion for CAT Exam
Ratios and proportions are fundamental to student knowledge in a variety of math and science topics. They’re essential for understanding slope, constant rate of change, and comparable figures in mathematics, which are all fundamental algebraic concepts and skills.
Conclusion
A ratio is a comparison of two quantities that is calculated by dividing one by the other. The quotient ab is considered the ratio between a and b only when a and b are two values of the same type and with same units, and b is not equal to 0. Ratios are denoted by the colon sign (:). This implies that the result ab does not have a unit and can be represented as a: b. The proportion of two equivalent ratios is always the same. Proportions are represented by the symbol (::) and aid in the calculation of undetermined values. To put it another way, proportion is an equation or statement which shows that two ratios or fractions are equal. If a: b = c: d, 4 non-zero values, a, b, c, and d, are said to be in proportion.
