If x and y are the numbers of ten’s and unit’s place of a two digit number(xy). If y is halved and x is doubled, the number obtained is equal to the number yx (i.e., interchange the digits of xy). Then the relation between x and y is:
Given that the ten’s and unit’s digit is x and y respectively.
Then the number = 10x + y.
The number obtained by interchanging the digits = 10y + x.
If y is halved (y/2) and x is doubled then the new number is 10(2x) + y/2
But the new number is equal to the number obtained by interchanging the digits.
Therefore, 10(2x) + y/2 = 10y+x
20x - x = 19y / 2
19x = 19y / 2
x = y/2
y = 2x
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