If the sum of the digits of any number, lying between 100

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If the sum of the digits of any number, lying between 100 and 1000 is subtracted from the
number, then the difference is always divisible by

1. 7
2. 9
3. 11
4. 6

Correct Option: B

Any number between 100 and 1000 may be written as 100m + 10n + K where 0 < m <
9, 0 < n < 9 and 0 < K < 9.
∴ (100m + 10n + K) – (m + n + K) = 99m + 9n = 9 (11m + n) = multiplie of 9.
Hence divisible by 9.