Question

The mean of five numbers is 27. If one of the numbers is excluded, the mean gets reduced by 2. What is the excluded number? ​

Answer 1

       $\underline{\bold{Solution:}}$

       $\text{Let the five numbers be }a,b,c,d,e$

$\implies \text{Mean} =\dfrac{a+b+c+d+e}{5} = 27$

$\implies a+b+c+d+e = 27\times5 = 135 \text{ ------ (i)}$

       $\text{Let }e \text{ be the excluded number}$

$\implies \text{New mean} = \dfrac{a+b+c+d}{4} = \text{Mean }- 2$

$\implies \dfrac{a+b+c+d}{4} = 27-2 = 25$

$\implies a+b+c+d = 25(4) = 100 \text{ ------ (ii)}$

       $\text{Substracting (ii) from (i)}$

$\implies a + b + c +d +e - (a + b + c + d) = 135 - 100$

$\implies a + b +c +d + e - a - b - c - d = 35$

$\implies e = 35$

 $\therefore \text{ }\text{ }\boxed{\text{The excluded number is }35}$