Q89 of 113 Page 110

Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.

Let the number be

Then


According to the question


10x + y = (10y + x)-9


10x + y = 10y + x-


10x-x + y-10y = -9


9x-9y = -9


x-y = -1⋯(ii)


Adding both equations (i) and (ii)


x + y + x-y = 11-1


2x = 10


x = 5


Put value of x in equation (i)


x + y = 11


5 + y = 11


y = 11-5


y = 6


Hence the number is xy = 56


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