Given:
The ratio between a two-digit number and the sum of the digits of that number is 4:1
The digit in the unit's place is 3 more than the digit in the ten's place
Let the digit in the ten's place be x.
Then the digit in the unit's place is x + 3 and the sum of the digits is 2x + 3.
The two-digit number can be expressed as:
10x + (x + 3) = 11x + 3
The ratio of the number to the sum of its digits is given by:
(11x + 3) / (2x + 3) = 4/1
Solve for x:
3x = 9
x = 3
Therefore, the two-digit number is 11x + 3 = 11(3) + 3 = 36.