A two-digit number is such that the ten's digit exceeds twice the unit's digit by 2 and the number obtained by interchanging the digits is 5 more than three times the sum of the digits. Find the two-digits number?

Let the digit in the unit's place be y and digit in the ten's place be x.
∴ Number = 10x + y
Then, x = 2y + 2
⇒ x - 2y - 2 = 0 ...(i)
Number obtained by reversing the digits = 10y + x
Then, 10y + x = 5 + 3(x + y)
⇒ 2x - 7y + 5 = 0 ...(ii)
On multiplying Eq.(i) by 2 and then subtracting it from Eq. (ii), we get y = 3
On substituting the value of y in Eq.(i), we get x = 8
So, the two-digit number is 83.