**Important**

**Shortcut**

**Formulas related to AVERAGE**

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__WWW.GovtJobsPortal.IN__**Average:**An average or arithmetic mean of given n number of items is a total sum divided by total number of items given.

**Therefore,**Average= Sum of Total Items Given/Number of Items

Let’s say If
we have Given n Items: n1, n2, n3, ….n

Then, Total Average=

n

__n1+n2+n3+----+n__n

**Important Formulas:**

·
When a person
covers the equal amount of distance at two different intervals of speed, Let’s say one at x km/h and
y km/h respectively, Then

**Total Average Speed**= (2xy)/(x+y)

·
When a
person covers the equal amount of distance at three different intervals of speed
one at x km/h & others two at y km/h and z km/h
respectively, Then

**Total Average Speed**= (3xyz)/(xy+yz+zx)

·
If we have
given the average of n items equal to x and average of n’ items equal to x’,
then,

**Total Average (n+n’)**will be =

__(nx+n’x’)__

__(__n+n’)

·
Let’s say
there are total x members in a family & their total average age is y years.
Then a new member joins the family and the new average age of the family
becomes n, then the a

**ge of new member**that joins the family will be =[n+x(n-y)] years
·
Let’s say
there are total x members in a family & their total average age is y years.
Then a member leaves the family and the new average age of the family becomes
n, then the

**age of that member**will be =[n-x(y-n)] years
·
To Find the Average
of first x consecutive natural numbers =(x+1)/2

·
To Find the Average
of first x natural Even numbers =(x+1)

·
To Find the Average
of natural even numbers up to x =(x/2)+1

·
To Find the Average of first x natural odd numbers= x

·
To Find the Average of natural odd numbers up to x = (x+1)/2

Important
Points to be Remember:

1. If the value
of each item is increased by the same value let’s say x, then their total average
will also be increase by that same value x.

2.
If the value
of each given item is decreased by the same value let’s say x, then their
total average will also be decrease by that same value x.

3.
If the value
of each given item is multiplied by the same value let’s say x, then their
total average will also be get multiplied by that same value x.

4.
If the value
of each given item is divided by the same value let’s say x, then
their total average will also be get divided by that same value x.

**Let’s Take an Example Now:**

Q) If the average
age of 20 students in a class given is 16 & When a teacher joins the class
then their average age increases by 1. Then what will be teacher’s age?

Normal
Method:

[Total No.
of students × Average Age] – [Total No. of Students including teacher) ×
Average Age (Including Teacher)]= Answer.

Therefore,
According to Question We get

20×16= 320

21×17= 357,

357-320= 37.

Therefore, 37
years will be the required answer.

Shortcut
Method:

[n+x(n-y)]
years ( As
According to the Formula Given Above )

Where,

n= new Average Age

x=Number of Students

y= Previous Average Age

Therefore, we get

= [17+20(17-16)]

= 17 + 20

=37

*Therefore 37 years will be the required answer.*
Thank You !! J

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