# 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 = • ## ESE and GATE ECE Online Classroom Program (24+ Live classes and 150+ mock tests)

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