CAT Average, Ratio and Proportion: Check Concept, Important Formulas, Solved Question, Preparation Tips
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CAT Average, Ratio and Proportion is one of the most common parts in the section of arithmetic in Quantitative Aptitude. The questions based on ratio and proportion are easy to solve. In CAT 2021, around 2 to 3 questions can be expected from this section. Both MCQ or TITA type questions can be asked from this topic, therefore candidates are advised to download previous year question papers to get an idea about the questions that might get asked in the paper. Download CAT Question Papers
Read the article to know more about the basic concepts, properties, difference and important formulas required to solve the questions based on ratio and proportion
Basic Concepts of CAT Average, Ratio & Proportion
- In Mathematics, the average is the single number that one can get by adding two or more numbers together and then divide the sum of these numbers by the number of figures added.
- As an example, say the average of 3 and 5 will be (3+5)/2 = 8/2 = 4.
- A ratio is defined as an ordered pair of numbers i.e a and b, which is written as a / b in which b is not equal to 0.
- For instance, for a boy and 3 girls the ratio will be 1 : 3.
- On the other side, a proportion can be explained as an equation where two different ratios are set and both are equal to each other.
- For example, ⅔ = 4/6 = 6/9.
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CAT Important Formulas for Ratio and Proportion
Below are some formulas used in CAT Average, Ratio and Proportion are listed.
| Terms | Formulas |
|---|---|
| Ratio Formula | a: b ⇒ a/b |
| Proportion Formula | a/b = c/d or a : b :: c : d |
| Fourth, Third and Mean Proportional | If a : b = c : d, then:
|
Properties of Proportion
| Terms | Properties |
|---|---|
| Proportion rule | a:b::c:d⇒ab=cd |
| Dividendo | if a:b = c:d then a - b:b = c - d:d |
| Componendo | if a:b = c:d then a + b:b = c + d:d |
| Alternendo | if a:b = c:d then a:c = b:d |
| Addendo | if a:b = c:d then a + c = b + d |
| Subtrendo | if a:b = c:d then a - c = b - d |
| Invertendo | if a:b = c:d then b:a = d:c |
| Componendo | if a:b = c:d then a + b:a - b = c + d:c - d |
| Average of ‘n’ consecutive Natural Numbers | ( n+1)/2 |
| Average of the square of consecutive n natural numbers | (n+1)(2n+1)/6 |
Tricks for Rations and Proportions
- If a/b = x/y, then ay = bx
- If a/b = x/y, then a/x = b/y
- If a/b = x/y, then b/a = y/x
- If a/b = x/y, then (a+b)/b = (x+y)/y
- If a/b = x/y, then (a-b)/b = (x-y)/y
- If a/b = x/y, then (a+b)/ (a-b) = (x+y)/(x-y), which is known as componendo -Dividendo Rule
CAT Sample Questions on Average, Ratio and Proportion
In the below section, some solved questions regarding CAT Average, Ratio and Proportion are given.
Ques. There are 2 tanks with the same volume. Both the tanks are full of oil and water. At first, the ratio of oil and water is 5:8 and secondly, the ratio of both is 7:19. Find out the ratio of the oil and water when both the tanks are poured in a larger tank.
- 1:3
- 17:52
- 151:304
- 17:35
Correct Answer: ( D)
Ques. The ratio of a two-digit natural number to a number formed by reversing its digits is 4 : 7. Calculate the sum of all the numbers of all those pairs from the following list.
- 99
- 198
- 330
- 132
Correct Answer: ( C)
Ques. INR 432 is divided among three workers named A, B and C so that 8 times A’s share = 12 times B’s share = 6 times C’s share. Find out the amount A will get.
- 122
- 144
- 143
- 153
Correct Answer: ( B)
Ques. In a mixture of milk and water i.e 35 L, the ratio of milk to water is 4:1. The ratio of milk to water totally changed when 7 L water was added to that milk and water mixture. To bring back the primary ratio of milk and water, what quantity of milk needs to be added now?
- 28L
- 25L
- 26L
- 24L
Correct Answer: ( A)
Ques. A boy covered a distance of 1,000 km in 16 hr in total. He covered that distance in a taxi at 36 km/hr and also in a bus at 80 km/hr. What is the distance covered by the bus?
- 770 km
- 640 km
- 720 km
- 680 km
Correct Answer: ( C)
Ques. In a bottle of liquor, there are ¾ of liquor and the remaining is water. Find out the quantity of the mixture taken away and equal quantity of water to remain half liqueur and half water?
- 1/3
- 1/2
- 1/4
- 1/5
Correct Answer: ( A)
Ques.The weight of a lump of two metals is 18gm and is worth INR 87. The value can be INR 78.6 when their weights are interchanged. What is the weight of the other metal in the mixture when the price of one metal is INR 6.7 per gram?
- 8grm
- 5grm
- 6grm
- 7grm
Correct Answer: ( A)
Ques. What is the outcome by dividing INR 60 in the ratio 1:2 between Mike and John?
- INR 4
- INR 5
- INR 6
- INR 7
Correct Answer: ( A)
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CAT Preparation Tips for Average, Ratio and Proportion
In the below section, some tips for the preparation of CAT Average, Ratio and Proportion are given.
- Must be well versed with the basic concept and all the formulas
- Note down the formulas with the example and practice daily
- After going through the question, try to understand it carefully
- Know the terms of all the sections
- Do practice the question from the previous year’s paper
- Give mock test more than twice in a week
Some Key Points to Remember
- Ratio is used when there is a comparison in the size of two things whereas proportion is used to show the relation between two rations.
- Proportion is always an equation.
- Ration can be represented as : and proportion can be represented as ::
While solving questions on ratio and proportion candidates can identify ratio questions if they see the term ‘to every’ in the questions whereas questions on proportion can be identified with the term ‘out of’.
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*The article might have information for the previous academic years, please refer the official website of the exam.