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Averages, Ratio And Proportion Questions For CAT 2025
Averages, Ratio and Proportion is one of the most commonly asked topics in the Quant section of the CAT exam. If you understand this topic well, it not only helps you solve direct questions but also makes it easier to answer problems from other topics like Mixtures, Time and Work, Profit and Loss, and Data Interpretation.
Below, we’ve shared some of the most important questions from this topic that are likely to appear in CAT 2025. These questions are perfect for practice and range from basic to moderate difficulty levels.
Important Formulas for CAT Averages, Ratio And Proportion Questions
Here we have shared the important CAT Averages, Ratio and Proportion formulas in a very simple and easy way. These formulas will help you solve questions faster and more accurately in the exam. You can also download the free formula PDF to practice and revise these topics anytime.
CAT Ratio and Proportion Formulae PDF
CAT Ratio and Proportion Formulas
| Concept | Formula / Explanation |
|---|---|
| Basic Ratio to Fraction | If a:b=c:da : b = c : d, then ab=cd\frac{a}{b} = \frac{c}{d} or ad=bcad = bc |
| Dividing in a Given Ratio | A’s share = aa+b×Total\frac{a}{a + b} \times \text{Total} B’s share = ba+b×Total\frac{b}{a + b} \times \text{Total} |
| Combining Two Ratios | If a:b=x:ya : b = x : y and b:c=y:zb : c = y : z, then a:b:c=x:y:za : b : c = x : y : z |
| Inverse Proportion | If one value increases and the other decreases: x1×y1=x2×y2x_1 \times y_1 = x_2 \times y_2 |
| Direct Proportion | If both values increase or decrease together: x1y1=x2y2\frac{x_1}{y_1} = \frac{x_2}{y_2} |
| Ratio of Work and Time | Work is inversely proportional to time: A takes 5 days, B takes 10 days → Work ratio = 2:12 : 1 |
CAT Averages Formulas
| Concept | Formula / Explanation |
|---|---|
| Basic Average Formula | Average=Sum of valuesNumber of values\text{Average} = \frac{\text{Sum of values}}{\text{Number of values}} |
| Finding Total from Average | Total Sum=Average×Number of values\text{Total Sum} = \text{Average} \times \text{Number of values} |
| Weighted Average (Combined Groups) | Weighted Average=(w1×a1)+(w2×a2)w1+w2\text{Weighted Average} = \frac{(w_1 \times a_1) + (w_2 \times a_2)}{w_1 + w_2} Where w1,w2w_1, w_2 are the number of items and a1,a2a_1, a_2 are their averages |
| Finding Missing Value | Missing number=(New Average×(n+1))−Sum of known values\text{Missing number} = (\text{New Average} \times (n+1)) - \text{Sum of known values} |
| When a Person Joins or Leaves | Change in average=Difference between the person’s value and original averageTotal number of people\text{Change in average} = \frac{\text{Difference between the person’s value and original average}}{\text{Total number of people}} |
Common Mistakes to Avoid in Ratio And Proportion Questions
Students often make small mistakes in Ratio and Proportion questions that can cost them valuable marks in the CAT exam. Be careful of these common errors:
Mixing different units: Always compare the same types of quantities (like kg with kg, not kg with litres)
Wrong total parts: When dividing ₹1000 in the ratio 2:3, make sure to add both parts (2 + 3 = 5) before calculating
Not simplifying ratios: Always simplify the ratio first — it makes the question easier to solve
Assuming real values: Ratios show comparison, not actual numbers — don’t guess values unless given
Misreading words like ‘more than’ or ‘less than’: Read the question carefully to avoid confusion in wording
Question 1
Consider the set S = {2, 3, 4, ...., 2n+1}, where n is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X - Y ?
correct answer:- 2
Question 2
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
Question 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
Question 4
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
Question 5
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
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correct answer:- 15
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