Login
Register
- Mocks
- Previous Papers
- Learn
- Practice
- Colleges
- Courses
- Enroll To CAT 2025
- Tools
- Offers
- Other Exams
- Blogs
- Adda
Averages, Ratios and Proportions are the parts of Arithmetic. The questions from these topics have been asked frequently in the Quantitative section of the CAT exam. Averages, Ratios and Proportions are the topics which deal with real-life scenarios. Having a firm grasp of Basics & Formulas is imperative to solve the questions from these topics. If we look at the CAT previous papers, Ratio, Proportions and Averages have made a recurrent appearance in the CAT Quant Section. It is a very important topic and hence must not be avoided by the aspirants. Take 3 Free CAT Mock Tests which will help you know where you currently stand, and will help you in analysing your strengths and weaknesses.
To help the aspirants ace this topic, we provide you with all the questions with detailed video solutions, which are given below, separated year-wise. One can also download all the CAT previous Questions from Averages, Ratios and Proportions in a PDF format, along with the video solution for every question.
Note: No Sign-Up is required to download the PDF
Year | Weightage |
| 2024 | 12 |
| 2023 | 7 |
2022 | 13 |
2021 | 14 |
2020 | 5 |
2019 | 10 |
2018 | 12 |
CAT Ratio & Proportions - Tip 1: Questions based on this concept appear in the CAT and other MBA entrance exams every year. If you're starting the prep, firstly understand the CAT exam syllabus; Based on our analysis of Ratio Proportion and Variation questions in CAT Previous Years this was the CAT Ratios, Averages, and Mixtures weightage: 4-5 questions were asked from these topics (in CAT 2021).
CAT Ratio & Proportions - Tip 2: The CAT Ratio and proportion questions are Not very tough to solve. A strong foundation in this topic will help you in answering these questions with ease. Getting yourself acquainted with the basics of these concepts will help you solve the problems. Download this ratio proportion and variation questions with solutions PDF (which also includes the ratio and proportion concept PDF). Learn all the major formulae from these concepts (You can learn all the Important CAT Ratios & Proportions Formulas here). Also, do check out the ratio and proportion questions from CAT Mock tests.
One of the important topics is Ratio and Proportion, which is essential for solving many mathematical problems. Understanding the formulas and concepts related to Ratio and Proportion can significantly improve the chances of scoring high in the CAT exam. And, enrolling in a CAT online coaching will help you grasp the fundamentals easily. The CAT Averages, Ratio and Proportion Formulas PDF is a valuable resource that provides a comprehensive overview of the formulas and concepts related to Ratio and Proportion. Click on the below link to download CAT Averages, Ratio and proportion formulas PDF.
1. Mixture of mixtures Formula
In a mixture of mixtures, two quantities of some mixtures are mixed to get a mixture of mixtures.
Let Mixture 1 have ingredients A and B in ratio a: b, and Mixture 2 have ingredients A and B in ratio x : y.
Now, the M unit of mixture 1 and N unit of mixture 2 are mixed to form a resultant mixture. Then, in the resultant mixture, the ratio of A and B is
$$\dfrac{Q_a}{Q_b}=\ \dfrac{M\left(\frac{a}{a+b}\right)+N\left(\frac{x}{x+y}\right)\ }{M\left(\frac{b}{a+b}\right)+N\left(\frac{x}{x+y}\right)}$$
2. Replacement of solution Formula
If a container has 'a' liters of liquid A and if 'b' liters of solution is withdrawn and is replaced with an equal volume of another liquid B and the operation is repeated for 'n' times, then after nth operation,
The final quantity of Liquid A in the container = $$\left(\ \frac{\ a-b}{a}\right)^{^n}\times\ a$$
3. Alligation Formula
Alligation Rule: This is used to find the ratio of individual components in a mixture. If two components A and B, costing Rs. X and Rs. Y individually, are mixed and the resultant mixture has an average price of Rs. Z, then the ratio of A and B in the mixture is $$\frac{Z-Y}{X-Z}$$
4. Weighted Average Formula
The weighted average of n terms equals $$\frac{w_1*x_1+ w_2*x_2+. . .+ w_n*x_n}{ w_1+ w_2+ . . . w_n}$$
In a group of 250 students, the percentage of girls was at least 44% and at most 60%.The rest of the students were boys. Each student opted for either swimming or running or both. If 50% of the boys and 80% of the girls opted for swimming while 70%of the boys and 60% of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are
correct answer:-3
A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is
correct answer:-340
When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima's age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become
correct answer:-3
In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 ∶ 6 ∶ 5. They rent a house together, and Kamal pays 15%, Amal pays 12% and Vimal pays 18% of their respective incomes to cover the total house rent in that month. In October, the house rent remains unchanged while their incomes increase by 10%, 12% and 15%, respectively. In October, the percentage of their total income that will be paid as house rent, is nearest to
correct answer:-2
A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was Rs. 60000, and of the first 10 and last 10 employees together was Rs. 50000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year 2023 was
correct answer:-1
A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes and half of the oranges, the ratio of number of unsold apples to number of unsold oranges becomes 3 : 2. The total number of unsold fruits is
correct answer:-66
There are four numbers such that average of first two numbers is 1 more than the first number, average of first three numbers is 2 more than average of first two numbers, and average of first four numbers is 3 more than average of first three numbers. Then, the difference between the largest and the smallest numbers, is
correct answer:-15
Rajesh and Vimal own 20 hectares and 30 hectares of agricultural land, respectively, which are entirely covered by wheat and mustard crops. The cultivation area of wheat and mustard in the land owned by Vimal are in the ratio of 5 : 3. If the total cultivation area of wheat and mustard are in the ratio 11 : 9, then the ratio of cultivation area of wheat and mustard in the land owned by Rajesh is
correct answer:-2
A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is
correct answer:-3
The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is
correct answer:-4
There are three persons A, B and C in a room. If a person D joins the room, the average weight of the persons in the room reduces by x kg. Instead of D, if person E joins the room, the average weight of the persons in the room increases by 2x kg. If the weight of E is 12 kg more than that of D, then the value of x is
correct answer:-3
In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the nonmanufacturing employees is
correct answer:-2
The salaries of three friends Sita, Gita and Mita are initially in the ratio 5 : 6 : 7, respectively. In the first year, they get salary hikes of 20%, 25% and 20%, respectively. In the second year, Sita and Mita get salary hikes of 40% and 25%, respectively, and the salary of Gita becomes equal to the mean salary of the three friends. The salary hike of Gita in the second year is
correct answer:-3
In a village, the ratio of number of males to females is 5 : 4. The ratio of number of literate males to literate females is 2 : 3. The ratio of the number of illiterate males to illiterate females is 4 : 3. If 3600 males in the village are literate, then the total number of females in the village is
correct answer:-43200
The average weight of students in a class increases by 600 gm when some new students join the class. If the average weight of the new students is 3 kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is
correct answer:-3
Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine months, his monthly expense was ₹3500, and he foresees that, tenth month onward, his monthly expense will increase to ₹3700. In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be
correct answer:-1
In an election, there were four candidates and 80% of the registered voters casted their votes. One of the candidates received 30% of the casted votes while the other three candidates received the remaining casted votes in the proportion 1 : 2 : 3. If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was
correct answer:-4
In an examination, the average marks of students in sections A and B are 32 and 60, respectively. The number of students in section A is 10 less than that in section B. If the average marks of all the students across both the sections combined is an integer, then the difference between the maximum and minimum possible number of students in section A is
correct answer:-63
The average of three integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is
correct answer:-3
If a and b are non-negative real numbers such that a+ 2b = 6, then the average of the maximum and minimum possible values of (a+ b) is
correct answer:-4
Video solutions can be a helpful resource for candidates preparing for CAT Averages, Ratios and Proportions questions. They can provide a step-by-step explanation of how to solve the problem, helping candidates better understand the concept and formula.
