The average of five consecutive numbers is x. If the next two numbers are included, how shall the average vary?

Solution(By Examveda Team)

Let the five consecutive numbers be z, z + 1, z + 3 and z + 4
Then,
$$ \Rightarrow \frac{{z + \left( {z + 1} \right) + \left( {z + 2} \right) + \left( {z + 3} \right) + \left( {z + 4} \right)}}{5} = x$$
$$\eqalign{ & \Rightarrow 5z + 10 = 5x \cr & \Rightarrow z = \frac{{5x - 10}}{5} \cr & \Rightarrow z = x - 2 \cr} $$
So, the numbers are x - 2, x - 1, x, x + 1, x + 2
∴ Required mean
$$ = \frac{{\left( {x - 2} \right) + \left( {x - 1} \right) + x + \left( {x + 1} \right) + \left( {x + 2} \right) + \left( {x + 3} \right) + \left( {x + 4} \right)}}{7}$$
$$\eqalign{ & = \frac{{7x + 7}}{7} \cr & = x + 1 \cr} $$