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

(a) Let suppose missing digit = x

Calculate the sum of the digits at odd places = 9 + 3 + 2 = 14

Calculate the sum of the digits at even places = 8+ x + 9 = 17 + x

Difference = 17 + x – 14 = 3 + x

For a number to be divisible by 11, this difference should be 0 or a multiplier of 11.

If 3 + x = 0, then

x = -3

But the number can not be negative.

A closest multiplier of 11, which is near to 3 is taken. This is 11 it self.

3 + x = 11

x = 8

Therefore, the required digit is 8.

(b) Let suppose missing digit = x

Calculate the sum of the digits at odd places = 4 + 4 + x = 8 + x

Calculate the sum of the digits at even places = 8 + 9 + 8 = 25

Difference = 25 – (8 + x) = 17 – x

For a number to be divisible by 11, this difference should be 0 or a multiplier of 11.

If 17 - x = 0, then

x = 17

But this is not possible.

A closest multiplier of 11 is taken, taking 11 it self we get,

17 - x = 11

x = 6

Therefore, the required digit is 6.