Question

Raj picks up a three digit number and subtracts it from the same number after reversing order of the digits. If the difference is divided by 9, then the remainder is ____________.
1. 2
2. 0
3. 1
4. 3

Answer 1

Correct Answer - Option 2 : 0

Concept:

The difference of any three-digit number by its reversing number is always an exact product of 9 So, it is divisible by 9.

Calculation:

Let 100x + 10y + z be the number its reverse is 100z + 10y + x

Difference of the number will be

⇒ (100z + 10y + x) − (100x + 10y + z)

⇒ (100 − 1)z + (10 − 10)y + (1 − 100)x

⇒ 99z − 99x = 99(z − x)

So the difference of any three-digit number with its reverse number is divisible by 9 then the remainder is 0

∴ Remainder is 0