linear equation

Let X and Y be the digits, then the number is 10X + Y.

8(X + Y) =  10X + Y  .....(1)

which simplifies to,

2X -7Y = 0

2X = 7Y    

Hence X + Y = 7Y/2 + Y = 9Y/2    ... (2)

Now the number formed by reversing the digits, 10Y + X.

Hence we can write (1), as, adding 9Y and Subtracting 9X from both sides,

8(X + Y) + 9Y - 9X =  10X + Y  + 9Y - 9X

-X  + 17Y = 10Y + X

-7Y/2 + 17Y = 10Y + X

27Y/2 = 10Y + X

3(9Y/2) = 10Y + X.                 ,,, using (2)

But 9Y/2 = X + Y = sum of digits,

3(X + Y) = 10Y + X.

Hence proved.

Regards,

Team,

TopperLearning.