Here are some of the Average shortcut formulas which will help you solve Average problems quickly and easily.

What is Average of Numbers?

What is Average of Numbers?

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

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

Hi Sir,Thankyou so much sir for posting tricks on various questions which is very helpful for us in competitive exams.Just now I came across the average shortcut formulas.Letters in this page is somewhat mismatching and x,y letters are placed on the other sentences.So requesting you to kindly clear that mismatches so that we can easily understand and solve the problems easily..

ReplyDeletethanks for the suggestion. as per your suggestion, the letters has been reverted to their last state. if you still have any problem, do write in comments

ReplyDeleteMany times its harder to remember formulas

ReplyDeleteyes but u have to do hard work to get desired results

Deleteif 8 students seated per bench,there will be 3 benches remaining and 5 students seated per bench 12 students left out then how many benches and students are there...can anyone give shortcut for such kind of questions please......

ReplyDeletelet there are x number of benches.

ReplyDeleteequating the number of students in both the arrangements,

8x-8(3)=5x+12

x=12

so number of benches=12

no. of students= 5x+12= 72

thnk u very much sir..pls post problems regarding progressions and more formulae on time and work,pipes and cistern..

ReplyDeleteDear Sir, please put some easy tricks for Pythagoras Theorem.

ReplyDelete