Question

If digits of two-digit numbers are interchanged then difference of the numbers is divisible by 
1. 11
2. 9
3. 6
4. 2

Answer 1

Correct Answer - Option 2 : 9

Concept:

Any number can be written as (digit × place value)

Ex:- 45 = 4 × 10 + 5 × 1 = 40 + 5

Calculation:

Let the two-digit number be 10x + y

Here x is tens digit and y is the unit digit

By interchanging the digits we'll get 10y + x

Difference of both numbers = (10x + y) – (10y + x) = 9x –  9y

⇒ Difference of both numbers = 9 × (x – y)

∴ Difference is divisible by 9

Example:- 

Let the number be 63

By reversing the digits we'll get 36

Difference = 63 – 36 = 27

27 is divisible by 9