## What are Ratio and Proportion CAT Questions?

To understand the ratio and proportion questions for the CAT exam, it is important to understand What is Ratio? And Is Ratio and Proportion the Same?

As per the mathematical concepts, ratio defines the correlation between two quantities, like A: B, in which B≠0. For example, the ratio of 3:6 is equal to 1:2. However, the statement is known as Proportion, and it is seen to be in direct Proportion.

Note the below example for conceptual clarity on what is ratio.

For example, 4/5 is a ratio and the proportion statement is 20/25 =4/5. If we find the proportional statement, we get the below things:

20/25 = 4/5

Therefore: 20 x 5 = 25 x 4, i.e., 100 = 100

In comparison, Proportion states the equality of 2 fractions in ratio.

It means that the Proportion is an equation that defines whether the two given ratios are equal or not. For example, the time taken by train to cover 100km per hour is equal to the time taken by it to cover the distance of 200km for 2 hours. Such as 100km/hr = 200km/2hrs.

So, the basic thing is that Ratio and Proportion are the two faces of a coin. If the value of the two ratios is the same, then it will be sailed to be in Proportion.

## Ratio and Proportion CAT Questions - Important Formula

Ratio and Proportion are two mathematical entities that assist in the comparison of numbers. Both are interrelated, and you must have conceptual clarity for the important formulas to solve Ratio and Proportion CAT Questions accurately.

Note the below sections to get an idea about the ratio and proportion formulas for the CAT Exam.

### Ratio Formula

Assume that you have two numbers, and you have to find the ratio of these two numbers. Then, as the definition of ratio, it will be A: B=A/B (Here, A and B are two numbers, and B is not equal to 0).

“A” is the first Term or antecedent, and “B” is called the second Term or consequent.

For example, the ratio 2:3 is represented as ⅔ (where 2 is antecedent and 3 is consequent)

### Proportion Formula

Assume that there are two ratios, A: B and C: D. Here, “B” and “C” are known as mean Terms, while “A” and “D” are called extreme terms.

For example: Let us consider one more example of several students in a classroom. Our first ratio of the number of girls to boys is 4:7, and that of the other is 3:5, then the Proportion can be written as:

4:7 :: 3:5 or 4/7 = 3/5

Here, 4 & 5 are the extremes, while 7 & 3 are the means.

Check the detailed CAT Syllabus for a better understanding

## How to Solve Ratio and Proportion Questions for CAT

The CAT questions on Ratio and Proportion can be solved easily and quickly by using some simple tricks and tips. In the following, our experts have listed shortcut tricks to solve Ratio and Proportion questions accurately.

- If A: B and C : D, then it can be solved as (A*C)/(B*D).
- If A/B=C/D=E/F, then each of these ratios is equal to (A+C+E) ⁄(B+D+F)
- If P/Q=S/T, then Q/P=T/S (Invertenao)
- If A/B=C/D, then A/C=B/D (Alterenao)
- If A/B=C/D, then (A+B)/B=(C+D)/D (Componendo)
- If P/Q=S/T, then (P-Q)/Q=(S-T)/T (Dividenao)
- If C/D=A/B, then (C+D)/(C-D)=(A+B)/(A-B) (Componendo and Dividendo)

## Sample Ratio and Proportion CAT Questions

Check the below questions to understand the difficulty level CAT questions on Ratio and Proportion.

**Example 1: **The average marks of Ravi in 10 papers are 80. If the lowest and highest scores in the exam are not considered, then the average is 81. If the highest score is 92, what is Ravi's lowest score?

- 60
- 55
- 62
- Cannot be determined

**Answer: **Correct answer is 60

**Solution:**

Total marks=80x10=800

Total marks without lowest and highest marks=81x8=648

So, the summation between lowest and highest marks= 800-648=152

Now the highest mark is 92, so, the lowest marks will be: 152-92= 60

**Example 2:** One bacterium split into eight bacteria of the next generation. But due to environmental condition, only 50% survives, and the remaining 50% dies after producing the next generation. If the 7th generation number is 4096 million, then find the number for the first generation.

- 2 million
- 4 million
- 1 million
- 8 million

**Answer: **The correct answer is 1 million

**Solution:**

Suppose the initial number of bacteria= x

So, in the 2nd generation, the number of bacteria=8x/2=4x

In the 3rd generation the number of bacteria= 16x

4th generation=64x

5th generation=256x

6th generation=1024x

7th generation=4096x

Hence, the value of x=1 million

You must be well-versed with all the basic concepts of Ratio and Proportion to solve its related questions accurately. Note the important formulas and practice previous year’s CAT questions daily to check your understanding level for CAT questions on Ratio and Proportion. The aspirants can also attend BYJU’S Exam Prep online classes to clear their doubts on Ratio and Proportion.

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