Question

The average (arithmetic mean) of y numbers is x. if 30 is added to the set of numbers, then the average will be x - 5. what is the value of y in terms of x ?

Answer 1

Given,

AM of y numbers = x.

Let the sum of y numbers be s.

AM of y numbers = x

$\frac{s}{y} = x$

$s = y*x$

Given, when 30 is added to the y numbers, the AM becomes x - 5.

$\frac{s + 30}{y + 1} = x - 5$

$\frac{y*x + 30}{y +1} = x - 5$

$y*x + 30 = (x -5)( y +1)$

$y*x + 30 = y*x + x - 5y -5$

$5y = x - 5 -30 = x - 35$

$y = \frac{x -35}{5}$