## Aug 25, 2015

### IMPORTANT SHORTCUT FORMULAS RELATED TO AVERAGE PROBLEMS

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Important Shortcut Formulas related to AVERAGE
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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= 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 age 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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