Write a digit in the blank space of the following number so that the number formed is divisible by $$11$$.
$$8$$___$$9484$$.
$$ 8 $$ ___$$ 9484 $$
let $$a$$ be placed in the blank.
Sum of the digits at odd places $$= 8+9+8=25$$
Sum of the digits at even place $$= 4+4+a=8+a $$
Difference $$= 25-(8+a) $$
$$ =17-a $$
For a number to be divisible by $$ 11$$, this difference should be zero or a multiple of $$ 11$$.
If $$ 17-a=0 $$, then
$$\Rightarrow a=17 $$
This is not possible
A multiple of $$ 11 $$ has to be taken. taking $$ 11 $$ we obtain
$$ 17-a=11 $$
$$\Rightarrow a=6 $$
Hence, the required digit is $$ 6 $$.