Question

In each of the following numbers, replace $M$ by the smallest whole number to make the resulting number divisible by $11$.
(iii) $7095M$

Answer 1

Step: Find value of $M$
Given number: $70975M$
A number is divisible by $11$, if the difference of the sum of its digits in odd places from the right side and the sum of digits in even places from the right side is divisible by $11$.
Here,
Sum of odd digits = $M+7+0=M+7$
Sum of even digits = $5+9+7$ = $21$
Difference = $21-(M+7)$ = $14–M$
Now, since $M$ is a whole number and we know that $0$ is divisible by $11$.
Thus, $14-M$ = $0$
⇒ $M$ = $14$.
Hence, the value of $M$ is $14$.