**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:

- x to y
- x:y
- 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:

- ::
- =

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

- Mean proportion
- Third proportion
- Fourth proportion: If three numbers a, b and c are given
- Direct Proportion
- Inverse Proportion

**The formula for Proportion:**

In order to find proportion for the two ratios, a:b and c:d. Then, a:b::c:d⟶ab=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 EE Online Classroom Program (24+ Live classes and 193+ mock tests)****ESE and GATE CE Online Classroom Program (24+ Live classes and 180+ mock tests)****ESE and GATE ME Online Classroom Program (24+ Live classes and 161+ mock tests)****ESE and GATE ECE Online Classroom Program (24+ Live classes and 150+ mock tests)**

Thanks

Sahi Prep Hai Toh Life Set Hai!

## Comments

write a comment