Average .........[competitive. exam prep.... topic 5]

Average Short Tricks:
The average of a number of items of the same type is their sum divided by the number of those items.
Average of consecutive first n natural numbers is
=(n+1)/2
Average of first n natural EVEN numbers is
=(n+1)
Average of natural even numbers up to n is
=(n/2)+1
Average of first n natural odd numbers is
=n
Average of natural odd numbers up to n is
=(n+1)/2
Average of n multiples of p will be
={p(n+1)}/2
----------------------------------
If a person covered a certain distance at a speed of x km/h and y km/h respectively, then his average speed will be
= (2xy)/(x+y)
If a person covers a certain distance at a speed of x km/h and y km/h and z km/h respectively, then his average speed will be
=(3xyz)/(xy+yz+zx)
If the average of n1 items is p1 and average of n2 items is p2 then the average of total items (n1+n2) will be
=(n1p1+n2p2)/(n1+n2)
The average of ages of x members of a family is y years. Now if a new member joins the family, then the new average of ages of all the members is z. then the age of new member will be
=[z-x(z-y)] years
The average of ages of x members of a family is y years. Now if a member leaves the family, then the new average of ages of all the members is z. then the age of that member will be
=[z+x(y-z)] years

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