The number obtained by interchanging the digits of a two-digit number is more than the original number by 27 and the sum of the digits is 13. What is the original number ?

Let the ten's place digit = x
and unit's place digit = y
∴ The original number = 10x + y
After interchanging the digits
Number will become 10y + x
∴ according to the given question,
y + x = 13 and
(10y + x ) - (10x + y) = 27
⇒ 9y - 9x = 27
⇒ y - x = 3 ................(i)
and y + x = 13 .................(ii)
On solving Eqs.(i) and (ii) , we get
y = 8 and x = 5
∴ Required number is
10x + y = 10 x 5 + 8 = 58