Best explanation to understand and solve the ratio and proposition

This section is about the aptitude questions based on RATIO AND PROPOSiTION. This topic will be familiar to most of you because you may have learned a lot about this in your schools.

It is one of the important topics in any aptitude exams. All the entrance exams and bank exams will have questions based on ratio and proposition.

It will be an easy task for you to solve the problems on ratio and proposition if you clearly understand the concept.

You must know the formulas for ratio and proposition, and also you should know the difference between ratio and proposition. 

This article will clearly explain you about the concept of ratio and proposition.

we also have provided some important formulas to solve the problems. Learn them and score high in your examinations.

What is ratio?

In mathematical terms,  ratio is a relationship between the given two numbers indicating how many times the first number contains the second one. Ratio is nothing but the fraction of two numbers.

We can take a ratio a : b, in which we call ‘a’ as the first term or antecedent and ‘b’, the second term or consequent.

For example:

if a bowl of vegetables contains eight carrots and ten cabbages, then the ratio of carrots to cabbages is eight to ten (that is, 8:10, which is equivalent to the ratio 4:5). Here, 4 is the antecedent and 5 is the consequent.

We can also express this fraction as 4 / 5

What is proposition?

A proposition is nothing but a statement that says true or false. It indicates whether the given two ratios are equivalent to each other.

For example,

If a : b = c : d, we can write it as  a : b :: c : d and we can say that a, b, c, d are in proportion.

In this proposition, a and d are called extremes and b and c are called mean terms.

Product of means = Product of extremes.

Thus, a : b :: c : d (b x c) = (a x d).

What is the difference between ratio and proposition?

The difference between ratio and proposition are as follows

Ratio can be defined as the comparison of sizes of two quantities of the same unit Proportion, on the other hand, refers to the equality of the given two ratios. 

In other terms, the ratio is an expression while proportion is an equation which can be solved. 

What are the rules of ratio?

Each and every term of the ratio must be divided or multiplied by the same non-zero number so that it does not affect the ratio.

What are the rules of proposition?

1.If there are 3 quantities like P, Q, and R and If they are a proportion, we can express them as

P: Q :: Q: R   

Or, P: QQ = Q: R

2.If there are 4 quantities like P, Q, R, and S and if they are a proportion, we can express them as

P: Q::R: S  

Or, P: Q = R: S  

Or, P* S = Q* R  

What are the important rules to remember to solve the problems on ratio and proposition?

  1. Fourth Proportional: If a : b = c : d, then d is known as the fourth proportional to a, b, c.
  2. Third Proportional: If a : b = c : d, then c in the given ratio is known as the third proportion to a and b.
  3. Mean Proportional: Mean proportional between the given ratio a and b is  ab

Comparison of Ration: We can say that (a : b) > (c : d)

5. Compounded Ratio: The compounded ratio of the given three ratios are (a : b), (c : d), (e : f) is (ace : bdf).

6. Duplicate Ratios:

  1. Duplicate ratio of the given ratio (a : b) is (a2 : b2).
  2. Sub-duplicate ratio of the given ratio (a : b) is (a : b).
  3. Triplicate ratio of the given ratio (a : b) is (a3 : b3).
  4. Sub-triplicate ratio of the given ratio (a : b) is (a1/3 : b1/3).

If ( a/b ) = ( c/d ) then ( a+b ) / ( a-b ) = ( c+d ) / ( c-d) [componendo and dividendo]

7. Variations:

  1. We say that x is directly proportional to y, if x = ky for some constant k and we write, x y.
  2. We say that x is inversely proportional to y, if xy = k for some constant k and

We write , x  ( 1/y )

What are the quick methods to solve the problems on ratio and proposition?

For example:

The income is divided between four person P, Q, R and S in the ratio 6:10:16:18 respectively. The share of S is 3744 more than the share of P. Find the total income of Q & R together?

Standard method to find the solution is

Let the total income = I

Sum or the ratios = 50

P’s share= (6/50) I, Q’s share= (10/50) I, R’s share= (16/50) I, S’s share= (18/50) I

And, S’ share = P’ share + 3744

Or, (18/50) I = (6/50) I + 3744

Or, (6/25) I = 3744

Or, I = 3744 x (25/6) = 15600

That means total income = 15600

Now, Q + R = (10/50)I + (16/50)I

Or, Q + R = (26/50) x 15600

Or, Q + R= 8112

Hence, we get the answer as 8112

But this method looks like time-consuming.

So the quick method to solve the ratio and proposition problem is

We know that

P’s share= 6 parts; Q’s share= 10 parts; R’s share= 16 parts and S’s share= 18 parts

ATQ, S – P = 3744 = 18 parts – 6 parts = 12 parts= 3744 

Or, 1 part = 3744/12 = 312


Q + R = 26 parts

Therefore the total income of Q + R = 26 x 312 = 8112 

We should always remember that we have to complete our exams before the given time. By using the standard method you will consume a lot of time.

But by using this quick method you can finish of the sum faster than the standard method’s timing.

But both the methods are correct while solving the problem. You may go with the method which is easy for you.

These are some important rules and quick methods that you should know before solving the problems on the aptitude ratio and proposition.

Hope this will be a very useful article. Now by using the given methods and rules try to solve the aptitude questions on our website. Because only practice can help you score high.