General Aptitude: Ratio & Proportion & Averages

By Asha Gupta|Updated : June 12th, 2021

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ratio & Proportion

Definition of Ratio:

Comparison of two different quantities having the same units. A ratio is read as "the ratio of x to y" but can be written or in three different forms:

  1. x to y
  2. x:y
  3. x/y

Types of Ratio:

Let us assume that, two numbers are "a" and "b". Then the ratio is a: b. Therefore,

  • Duplicate ratio
  • Sub duplicate ratio
  • Triplicate ratio
  • Sub triplicate ratio
  • Inverse ratio
  • Compounded ratio
  • Equivalent Ratio

 The formula for Ratio:

  • The formula for ratio is defined as a:b ⇒ a/b, where,
    “a” is called the first term or antecedent.
    “b” is called the second term or consequent.

Simplification:

  • Write the given ratio a:b in the form of a fraction a/b.
  • Find the greatest common factor of  'a' and "b".
  • Divide the numerator and denominator of the fraction with the GCF to obtain the simplified fraction.
  • Represent this fraction in the ratio form to get the result.
  • In case both the numbers 'a' and "b" are equal in the ratio a:  b, then a: b = 1.
  • If  a > b in the ratio a : b, then a : b  > 1.
  • If  a <  b in the ratio a : b, then a : b < 1.
  • It is to be ensured that the units of the two quantities are similar before comparing them.
  • In some cases-
    • Multiplying numerator and denominator by same number x.
    • Dividing numerator and denominator by same number y.

 Definition of Proportion:

If two ratios are equal then the 4 terms are called proportion. A proportion is read as "in proportion to" but can be written as:

  1.  ::
  2.  =

It can also be written as-   a: b:: c : d

Here terms a and d are called extremes and terms c and d are called means.

Types of Proportion:

If the ratio is a: b, then

  1. Mean proportion
  2. Third proportion
  3. Fourth proportion: If three numbers a, b and c are given
  4. Direct Proportion
  5. Inverse Proportion

The formula for Proportion:

In order to find proportion for the two ratios, a:b and c:d. Then, a:b::c:dab=cda:b::c:d⟶ab=cd

  • The two terms "b" and "c" are called ‘mean terms’.
  • The two terms ‘a’ and ‘d’ are known as ‘extreme terms.’

 Difference Between Ratio and Proportion:

Average 

Average is defined as “The sum of observations divided by the number of observations”. 

Important concepts: Here are some important points to remember,

1. When a person replaces another in a group of n persons with an average of group A, then -

  • If the average of the group is increased, then
    Age of new person = Age of person who left + (n × Increase in average) 
  • If the average of the group decreases, then
    Age of new person = Age of person who left – (n × Decrease in average)

2. When a person joins the group of n persons with an average of group A, then

  • If the average of the group is increased, then
    • Age of new person = Age of person who left + (n × Increase in average) 
  • If the average of the group decreases, then
    • Age of new person = Age of person who left – (n × Decrease in average)

3. When a person joins the group of n persons with an average of group A, then

  • If the average of the group is increased, then
    • Age of new member = Previous average + (n + 1) × Increase in average
  • When a person joins the group and the average of the group is decreases, then 
    • Age of new member = Previous average – (n + 1) × Decrease in average

4. When a person left the group of n persons with an average of group A, then

  • If the average of the group is increased, then
    • Age of new member = Previous average –  (n + 1) × Increase in average
  • When a person joins the group and the average of the group is decreases, then 
    • Age of new member = Previous average + (n + 1) × Decrease in average

 5. Average of the number of terms In an Arithmetic Progression

  • When the number of terms is odd:– The average will be the middle term.
  • When a number of terms are even:– The average will be the average of two middle terms.
  •  The sum of 1st n consecutive natural numbers = 

 

 

 

 

 

Thanks 
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Posted by:

Asha GuptaAsha GuptaMember since Mar 2021
Associate Content Developer - AE/JE Non-technical
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