If the digit in the unit's place of a two-digit number is halved and the digit in the ten's place is doubled, the number thus obtained is equal to the number obtained by interchanging the digits. Which of the following is definitely true ?

Let the ten's digit be x and the unit's digit be y
Then, number = 10x + y
New number :
$$\eqalign{ & = 10 \times 2x + \frac{y}{2} \cr & = 20x + \frac{y}{2} \cr} $$
$$\eqalign{ & \therefore 20x + \frac{y}{2} = 10y + x \cr & \Leftrightarrow 40x + y = 20y + 2x \cr & \Leftrightarrow 38x = 19y \cr & \Leftrightarrow y = 2x \cr} $$
So, the unit's digit is twice the ten's digit.