The digit in the unit's place of a numbers is equal to the digit in the ten's place of half of that number and the digit in the ten's place of that number is less than the digit in unit's place of half of the number by 1. If the sum of the digits of the number is 7, then what is the number ?

Let the ten's digit be x and unit's digit be y
Then,
$$\eqalign{ & \Leftrightarrow \frac{{10x + y}}{2} = 10y + \left( {x + 1} \right) \cr & \Leftrightarrow 10x + y = 20y + 2x + 2 \cr & \Leftrightarrow 8x - 19y = 2.....(i) \cr & {\text{And}} \Leftrightarrow x + y = 7.....(ii) \cr} $$
Solving (i) and (ii), we get :
x = 5, y = 2
Hence, required number = 52