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Q.6. 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


Answer :

(a) 92 ___ 389
Let, at the missing digit be x
Sum of the digits at odd places = 9 + 3 + 2 = 14
Sum of the digits at even places = 8 + x + 9 = 17
Difference = 17 + x – 14 = x + 3
For the given number to be divisible by 11
x + 3 = 11
x = 11 – 3 = 8
So, the missing digit = 8
Hence, the required number is 928389.
(b) 8 ___ 9484
Let the missing digit be x
Sum of the digits at odd places = 4 + 4 + x = 8 + x
Sum of the digits at even places = 8 + 9 + 8 = 25
? Difference = 25 – (8 + x)
= 25 – 8 – x = 17 – x
For the given number to be divisible by 11
17 – 0 = 11
\(\therefore \)17 – 11 = 6
So, the missing digit = 6
Hence, the required number = 869484.

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