# Ratio and Proportion Questions and Formula

Ratio and Proportion questions are is an important topic to be covered in competitive exams preparation be it for IBPS Clerk, PO, RRB, SO, or SBI Clerk or PO. The number of questions and the complexity of questions vary from exam to exam every year.

Ratio and Proportion questions are complex in nature and require an understanding of Numbers Systems, Squares and Square rootsCubes and Cube roots, and Math Tables. Examples of Ratio and Proportion Questions and Practice on Ratio and Proportion questions are given in this article.

Nowadays, questions in exams are mixed with multiple concepts and it requires practice and a deep understanding of basic concepts along with quickly identifying numbers.

## What is Ratio?

In many scenarios and many times, we need to compare two quantities or two numbers representing the same type. In other words, we can say that two quantities or numbers are compared in terms of “how many times” which is called Ratio and it’s represented by the symbol ‘:‘.

To Understand: If a Car cost 5,00,000/- and a Bus costs 20,00,000/- then in terms of cost if we have to find Car’s cost is what times to Bus cost. So we can say that the Bus is 4 times costlier than Car. In terms of Ratio, we can denote it as Car: Bus is equal to 1 : 4 times.

### Ration and Proportion Questions: Point to Remember

• Two quantities can be compared only if they are in the same unit.
• We can get equivalent ratios by multiplying or dividing the numerator and denominator by the same number.

## What is Proportion?

If we compare two ratios they are equal, then we say that they are in Proportion and denominate by the symbol ‘::’ or ‘=’ to equate the two ratios. In ration and proportion, the four quantities involved when taken in order are known as respective terms. The first and fourth terms are known as extreme terms. The second and third terms are known as middle terms.

For Example, 2, 4, 180, and 360 are in the proportion which is written as 2 : 4 :: 180 : 360 as we see 2 x 2 is 4 and the same as 2 x 180 is 360.

## Formula for Ratio and Proportion Questions

For understanding the formulas of Ratio and Proportion Questions we’ll denominate a = First Ratio, b = Second Ratio, c = Third Ratio, and d = Fourth Ratio.

a:b :: c:d

### 1st Formula: Mean Proportion

If ratio proportion is represented as a:b :: b:c then
b2 = a x c or we can say as b = √ac

For Example: If a = 16, b = ? and c = 4
substituting values in above formula
b2 = 16 x 4 or b = √(16 x 4)
b2 = 64 or b = √64
On finding square root we’ll get value of b.

### 2nd Formula: Continued Proportion

If ratio proportion is represented as a:b, b:c then
a:b:c will be (a x b) : (b x b) : (b x c)

For Example: If a:b = 4:2 and b:c = 1:2. Find value of a:b:c?
substituting values in above formula
=> (4 x 1) : (2 x 1) : (2 x 2)
=> 4:2:4 {we can simplify this by dividing 2.}
=> 2:1:2 is the value of a:b:c

## Solved Example of Ratio and Proportion Questions

Below are the solved examples of Ratio and Proportion Questions:

Example 1: Is the ratio 4:16 and 6:24 are in proportion?
=> 4:16 => 1:4 => 0.25
=> 6:24 => 1:4 => 0.25
From the above calculation, both ratios are the same and can be said in proportion.

Example 2: a:b = 3:5 and b:c = 3:2, Find a:b:c?
From the above formula we can calculate as below:
=> (3 x 3): (5 x 3): (5 x 2)
=> 9:15:10

Example 3: In ration a:b:c and a = 5 and b = 10 then find the value of c?
From the above formula we can calculate as below:
=> (10)2 = 5 x c
=> 100 = 5 x c
=> (100 / 5) = c
=> c = 20
Hence a:b:c = 5:10:20
Simplified form = 1:2:4

Example 4: In ratio and proportion a:b::c:d, if a = 3, b = 4, c = 15 then find value of d?
Substituting value in ratio and proportion, we get:
=> (3 / 4) = (15 / d)
=> d = (15 x 4) / 3
=> d = 60 / 3
=> d = 20

Example 5: If Ram can travel 80 kms in 4 hrs, then in 8 hrs how much distance he’ll cover?
Let’s substitute value in ratio and proportion, we’ll club same value of ratio.
Time Ratio = 4hrs : 8 hrs
Distance Ratio = 80 kms : x kms
Now, let’s find proportion of these ratios.
=> 4:8::80:x
=> x = (80 x 8) / 4
=> x = 640 / 4
=> x = 160

## Practice Ratio and Proportion Questions

Below are the Practice Ratio and Proportion Questions:

1. If a : b = 9 : 8 and b : c = 1 : 4. Then find a:b:c?
2. If a : b = 9 : 8, b : c = 1 : 4 and c : d = 1 : 2. Then find a:b:c:d?
3. If a : b = 9 : 12 and c : d = x : 16. Find value of x?
4. If a : b = 3 : 10 and c : d = 30 : x. Find value of x?
5. 2 : b : 18 Find the value of b?
6. 4 : b : 16 Find the value of b?
7. The speed of train A is 42 kmph and the speed of train B is 7 kmph. Write the ratio of train speed?
8. A motorbike travels 220 km in 5 liters of petrol. How much distance will it cover in 1.5 liters of petrol?
9. If the cost of 6 cans of juice is ` 210, then what will be the cost of 4 cans of juice?
10. The cost of 105 envelopes is 350. How many envelopes can be purchased for 100?

## FAQs

### What is Ratio?

Two quantities or numbers are compared in terms of “how many times” which is called Ratio and it’s represented by the symbol ‘:‘.

### What is Proportion?

When we compare two ratios they are equal, then we say that they are in Proportion and denominate by the symbol ‘::’ or ‘=’ to equate the two ratios.

### What is Mean Ratio?

If ratio and proportion is represented as a:b :: b:c then
b2 = a x c or we can say as b = √ac. b is the mean ratio.

### What is Continued Proportion?

On multiplying the first ratio by c and the second ratio by b, then the First ratio- ca:bc and the Second ratio- bc: bd. Hence, the continued proportion can be written in the form of ca: bc: bd

## Final Words

Practicing the above Ratio and Proportion questions is not the end of your practice, but it’s a start of a new journey to apply logic to Ratio and Proportion questions and solutions with multiple approaches to get the correct answer in a right and faster way.

For cracking competitive exams one must practice Ratio and Proportion questions without a calculator is a must. At last, during the exam, if a solution for the Ratio and Proportion question cannot be found easily then mark that question to revisit and move ahead instead of wasting time and energy.