Question

In each of the following replace * by a digit so that the number formed is divisible by 9
a) 12525*2 b) 251*3373

Answer 1

(a) $12525\ast 2$

First adding all the digits of the given number.

$\therefore 1+2+5+2+5+\ast +2=17+\ast$

For $12525\ast 2$ to be divisible by $9$, $17+\ast$ must be divisible by $9$.

Again adding the digits of $1+7+\ast$

$1+7+\ast =8+\ast$, which must be equal to $9$.

i.e., $8+\ast =9$

$\Rightarrow \ast =9-8=1$.

If $\ast =1,17+\ast =17+1=18$, which Is a multiple of $9$.

$\therefore 1252512$ is the required number.

(b) $251\ast 3373$

Firstly add the digits of the given number.

i.e., $2+5+1+\ast +3+3+7+3=24+\ast$, which must be a multiple of $9$

Again adding the digits of $24+\ast$

i.e., $2+4+\ast =6+\ast$ which must be equal to $9$.

i.e., $6+\ast =9$

$\Rightarrow \ast =9-6$

$\Rightarrow \ast =3$

If $\ast =3$, then $24+\ast =24+3=27$, which is a multiple of $9$.

$\therefore 25133373$ is the required number.