# Hadya's roll number is a two digit number. Her friend Hani's roll number has the same digits as Hadya's roll number, but with digits interchanged. If they add their roll number, and divide the sum by 11. Find the remainder of this division. (with explanation)

Dear Student,

Let , Unit place digit  =  x  and Ten's place digit =  y  , So

Hadya's roll number =  10 y  + x

As given : Hani's roll number has the same digits as Hadya's roll number, but with digits interchanged. So

Hani's roll number =  10 x  + y

Then , Sum of their roll number  =    10 y  + x +   10 x  + y =   11 x  + 11 = 11 ( x  + y  )

We can see sum of their roll number is multiple of 11  , So if we divide sum of their roll number by 11 we get " 0 " as remainder .

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Hi Sreeram, let x be the ten place and y be in unit place
So value of that roll number is 10 x + y
As we intechange them then Hani's roll number will be 10 y + x
Now adding their roll numbers we get 11 x + 11 y
Could be rewritten as 11 ( x+y)
So it is divisible by 11 and so remainder is 0
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What are you looking for?