Q. 64.0( 35 Votes )

Write a digit in

Answer :

(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 cannot be negative.


The closest multiplier of 11, which is near to 3 is taken. This is 11 itself.


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.


The closest multiplier of 11 is taken, taking 11 itself we get,


17 - x = 11


x = 6


Therefore, the required digit is 6.

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