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CAT Questions | CAT Arithmetic Questions: Ratio and Proportion

Ratio and Proportion carry high importance in management entrance exams like CAT, XAT, NMAT. It is an integral part of the Arithmetic chapter and holds great relevance in other sections like Data Interpretation in these entrance exams. Prior understanding of numbers, percentage calculation and fractions is a must to study this chapter. The fast numbers speed will help you in solving questions on ratio & proportion each time. Students can expect at least 1-2 questions from Ratio and Proportion. Hence, if you are planning to go for all kinds of management exams- Ratio and Proportion chapter has high importance in mathematics too.

CAT Quantitative Aptitude questions | CAT Arithmetic: Ratio and Proportion

Below you will find Ratio and Proportion questions that came in previous years’ CAT papers.


  1. A solution, of volume 40 litres, has dye and water in the proportion 2 : 3. Water is added to the solution to change this proportion to 2 : 5. If one-fourths of this diluted solution is taken out, how many litres of dye must be added to the remaining solution to bring the proportion back to 2 : 3? ______________

                                                                                                                                                           [CAT 2020]


1. Answer:


40 litres is split in ratio 2:3

So dye = 16 l and water = 24 l

Now proportion is 2:5

Already in the ratios 2:3

2 : 5

Now, 16 l of dye : 40 l of water

16 l of water is added

1414th is removed from the proportion

12 l of dye : 30 l of water

Now how many dye has to be added to make 2 : 3

2 : 3

12 l of dye : 30 l of water

Multiplication factor is 10 (3 × 10 = 30)

2 × 10 = 20 l of dye in total,

So 8 l of dye has to be added.

2.  A sum of money is split among Amal, Sunil and Mita so that the ratio of the shares of Amal and Sunil is 3:2, while the ratio of the shares of Sunil and Mita is 4:5. If the difference between the largest and the smallest of these three shares is Rs 400, Sunil’s share, in rupees, is ________

                                                                                                                                                           [CAT 2020]


2. Answer:


A : S : M

3 : 2

4 : 5

6 : 4 : 5

Given difference 6k – 4k = 2k = 400

k = 800

3.  Amala, Bina, and Gouri invest money in the ratio 3 : 4 : 5 in fixed deposits having respective annual interest rates in the ratio 6 : 5 : 4. What is their total interest income (in Rs) after a year, if Bina’s interest income exceeds Amala’s by Rs 250?

          A) 7250    B) 6350    C) 7000    D) 6000                                                                                    [CAT 2019]


3. Answer:

Ratio of their interest at the end of a year = 3*6 : 4*5 : 5*4 = 18 : 20:20
As per question 20x -18x = 250
2x = 250
X = 125
So total interest = (18+20+20)*x = 58*125 = 7250

 4.  Raju and Lalitha originally had marbles in the ratio 4:9. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5:6. What fraction of her original number of marbles was given by Lalitha to Raju?

          A) 1/4    B) 7/33    C) 1/5    D) 6/19                                                                                            [CAT 2018]


4. Answer:


Let the number of marbles with Raju and Lalitha initially be 4x and 9x. Let the number of marbles that Lalitha gave to Raju be y.

It has been given that (4x+y)/(9x-y) = 5/6 24x + 6y = 45x – 5y

11y = 21x

y/x = 21/11

Fraction of original marbles given to Raju by Lalitha = y/9x (As Lalitha had 9x marbles initially).

y/9x = 21/99

= 7/33

Basic Concepts in Ratio and Proportion:

There are some set concepts or types of Ratio and Proportion which questions are framed. A thorough understanding of each type of problem would help in tackling the exam. Questions based on Ratio and Proportion concepts in CAT, XAT, SNAP, NMAT, etc. are of the following type:

  • Concept of the ratio which can be defined as the ratio of the quantity A to the quantity B is a relation that tells us what multiple or fraction the quantity A is of the quantity B.
  • Comparison of ratios.
  • The concept of proportion can be defined as when 2 quantities are equal, the 4 quantities composing them are said to be proportional.
  • Operations on ratios.
  • Operations on proportions.
  • Direct and inverse proportions- when the amount of a certain entity increases when the amount of another entity increases, they are said to be in direct proportional to each other. And are depicted as ‘x∝y’ and if x increase, as y decreases, then they are inversely proportional to each other ‘x∝1/y’.

Preparation Phase for Ratio and Proportion:

Ratio Proportion questions forms the important part of Arithmetic which has good contribution in the Quants section of CAT, XAT, SNAP, NMAT and other various management entrance exams. We will divide the preparation of this topic into three levels following which can help the aspirants to score exceptionally well in problems of ratio and proportion what comes up in the management entrance exams.

Level I:

The student should first and foremost understand the basics of ratio and proportion and practice conversions from ratios to fraction form to percentage such as 0.25 is 25% which is in turn ¼. To learn thoroughly the calculations on tip of the tongue, Aspirants can practice questions from MBAP CAT E Book (Practise Questions) to speed up his/her calculations. If calculator is needed for complex calculations, do it in a timed manner and on the computer. At the present level, MBAP CAT E-book (Concept Theory) study material and MBAP Live Lecture Recording (Basic) can be referred to for brushing up the basics and practicing entry-level calculations.

Level II:

At this level, more focus should be on higher level ratio and proportion problems and solving them accurately and without looking at the solutions. The speed of solving the questions should not be focused on at this stage. An Excel sheet can be maintained to monitor the progress in the questions by the student. Any questions which are deemed to be difficult and can’t be solved in the first go should be recorded and revised after a week, if the difficulty is faced again, then the concept should be revised. For the intermediate level, study matter from MBAP Topic wise Previous Year CAT Question can be referred to as it has graded material with sections divided into different levels of difficulty.

Level III:

At the next level, the aspirant needs to focus on the speed on solving ratio and proportion examples and also solving them correctly and with accuracy without looking at solutions. Mocks should be given at this level. Several mocks should be given in an environment which is similar to the actual exam- without disturbance and in a timed manner. Use MBA CAT Advance E-books. A complete analysis needs to be carried out. Section- wise tests will have questions of varying difficulty, attempting questions of the same difficulty level is not conducive as the real exam is a mixture of questions of different difficulty levels. Making use of MBAP Previous year CAT paper will be beneficial which contains ratio and proportion questions and answers. The art of selecting which questions to attempt and which to leave un- attempted needs to be practiced now, also which topics should be attempted and which to leave is also identified right now.

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