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Average shortcut formulas-All types of average formulas

Here are some of the Average shortcut formulas which will help you solve Average problems quickly and easily.
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
                 ={p(n+1)}/2
CLICK HERE TO KNOW AVERAGE SHORTCUT TRICKS
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


7 comments:

  1. 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..

    ReplyDelete
  2. thanks 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

    ReplyDelete
  3. Many times its harder to remember formulas

    ReplyDelete
    Replies
    1. yes but u have to do hard work to get desired results

      Delete
  4. if 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......

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  5. let there are x number of benches.
    equating 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

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

    ReplyDelete

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