Question

The average of x numbers is 48. If 5/6 of the numbers are increased by 51 each and remaining are decreased by 71 each, then what is the new average?

Answer 1

Answer:

New average is 78.6667

Step-by-step explanation:

Let there are six numbers denoting by

x1 , x2 , x3 , x4 , x5  and x6

Now according given condition

average of numbers = ( x1 + x2 + x3 + x4 + x5 + x6 ) / 6 = 48     ......(1)

Since

(5 / 6) of number 6 = (5 / 6)×6 = 5

And

1 - (5 / 6) = 1

So We have to add 51 in five terms and subtract 71 from one term according to second condition given in the question.

Let add 51 in first five terms that is

 x1 , x2 , x3 , x4 , x5 becomes x1+51 , x2+51 , x3+51 , x4+51 , x5+51

and by subtracting 71 from last term

x6 becomes x6 - 7.

Now  let average of new formed numbers = A

then

A = (x1+51 + x2+51 + x3+51 + x4+51 + x5+51 + x6-7) / 6

  = (  x1 + x2 + x3 + x4 + x5 + x6 +51+51+51+51+51-71) / 6

  =  (  x1 + x2 + x3 + x4 + x5 + x6 + 184) / 6

  =   {(  x1 + x2 + x3 + x4 + x5 + x6 ) / 6 } + (184 / 6)

  = 48 + (184 /6)                                 ∵ we use equation (1) here

  = (48×6 + 184) /6

  = 78. 6667

  So

 A = 78.6667

and

New average is 78.6667

You can play same trick for any number of terms but you will get always new average equal to 78.6667