The difference of the number consisting of two digits and the number formed by interchanging the digits is always divisible by ? Explanation needed.
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A two digit number can be written as 10x + y,
where x is the digit at tens' place and y is the digit at ones' place.
On interchanging the digits, the number formed
= 10x + y
Therefore,
10x + y - (10y + x) = 9x - 9y = 9(x - y)10x+y−(10y+x)=9x−9y=9(x−y)
=> Given difference is always divisible by 9.
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