Question

In each of the following numbers, replace $M$ by the smallest whole number to make the resulting number divisible by $11$.
(iv) $14M75$

Answer 1

Step: Find the value of $M$
Given number: $14M75$

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 = $5+M+1$ =$6+M$
Sum of even digits =$7+4$= $11$
Difference = $11-(6+M)$ = $5–M$
Now, since $M$ is a whole number and we know that $0$ is divisible by $11$.
Thus, $5-M$ =$0$
⇒ $M$ = $5$
Hence, the value of $M$ is $5$.