Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11:
(a) 92 __ 389 

(b) 8 __ 9484

We know that as per the rule of divisibility by 11, if the difference between the sum of the digits in the number's odd and even places is zero or equal to 11, then the supplied number is also divisible by 11.

(a) 92 __ 389 
Let ‘m' be the missing digit.
Sum of digits at odd places = 9 + 3 + 2  = 14
Sum of digits at even places = 8 + m + 9  = 17 + m
Difference = 17 + m – 14  = 3 + m
By the divisibility rule, we have 3 + m = 0 and 3 + m = 11
If 3 + m = 0 gives m = -3, which is not possible as the digit cannot be negative.
Now, 3 + m = 11 gives m = 8.
So the required digit is 8.

(b) 8 __ 9484
Let ‘m' be the missing digit.
Sum of digits at odd places = 4 + 4 + m  = 8 + m
Sum of digits at even places = 8 + 9 + 8  = 25
Difference =  25 - (8 + m) = 17 - m
By the divisibility rule, we have 17 - m = 0 and 17 - m = 11
If 17 - m = 0 gives m = 17, which is not possible as we need one digit.
Now, 17 - m = 11 gives m = 6.
So the required digit is 6.