Question

Average of $6$ numbers is $8$, what number should be added to it to make the average $9$?

Answer 1

Average of 6 numbers is 8.

Let the 6 numbers be $a_1,a_2...a_6$

$\therefore \left(\sum _{i=1}^6{a}_{[}i\right])÷6=8$

$\Rightarrow \sum _{i=1}^6{a}_i=8\times 6$

$\Rightarrow \sum _{i=1}^6{a}_i=48$

If a 7th number is added to the existing 6 numbers,

then the average should be 9.

Let the 7 th number be $a_7.$

$\Rightarrow \left(\sum _{i=1}^7{a}_i\right)÷7=9$

$\Rightarrow \sum _{i=1}^6{a}_i+a_7=9\times 7$

$\Rightarrow a_7=63-48$

$\Rightarrow a_7=15$