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Ratio and Proportion Aptitude Concepts and Formulas

Points to Remember:

Ratio:

A ratio can be defined as the relationship between two numbers by the division of the same kind. i.e., Ratio of x and y is written as x: y = x/y. In x: y, we can say that x is the numerator and y is the denominator, or in other words, x as the antecedent, and y the consequent.

For example, the ratio of 7:3 can be represented as 7/3, so the numerator = 7, and denominator = 3 or we can say the antecedent = 7, and the consequent = 3

Rule of ratio:

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

Proportion:

A proportion refers to two ratios that are equivalent to each other.

For example: 7 /9 = 35/45. These two ratios form a proportion as they are equivalent to each other.

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

In case of 4 quantities like P, Q, R, and S, which are a proportion, we can express them as

Example of Ratio and Proportion:

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?

  • 8112
  • 4165
  • 8056
  • 7065

The standard method to Solve Ratio and Proportion sums:

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, but it looks like time-consuming.

Quick Method:

The above method may lead you to the correct answer but time management is the most important thing while solving the problems. The candidates need to try to solve the problems in the minimum possible time. Therefore, try this quick method which is faster than the standard way:

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
Now,
Q + R = 26 parts
So, the total income of Q + R = 26 x 312 = 8112  

Ratio and Proportion Aptitude Test Paper 1
Ratio and Proportion Aptitude Test Paper 2
Ratio and Proportion Aptitude Test Paper 3
Ratio and Proportion Aptitude Test Paper 4





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