If the sum of the digits of a three digit number is subtracted

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If the sum of the digits of a three digit number is subtracted from that number, then it will always be divisible by

1. 3 only
2. 9 only
3. Both 3 and 9
4. All of 3, 6 and 9

Correct Option: C

Let the 3–digit number be 100p + 10q + r.
Sum of the digits = p + q + r
According to the question ,
Difference = 100p + 10q + r – (p + q + r)
Difference = 99p + 9q
Difference = 9 (11p + q)
Clearly, it is a multiple of 3 and 9.
Hence required answer are 3 and 9.