Question

Write a digit in the blank space of the given number $8{,}_{-}9,487$ so that the number formed is divisible by $11$.

Answer 1

We know that A number is divisible by $11$, if the difference between the sum of digits at odd places and the sum of digits at even places is either $0$ or multiple of $11$.

Here, Sum of digits at odd places $=8+9+8=25$

And Sum of digits at even places $=7+4=11$

Since, the difference $=25–11=14$ is not a multiple of $11$. On adding $3$ to the blank space, sum of digits at even places will be $7+4+3=14$. Hence, new difference will be $25–14=11$ which is a multiple of $11$.

Therefore, the given number is divisible by $11$.