The sum of the dugits of …

Let the ten's digit of the required number be x and the unit's digit be y.
As per given condition the sum of the digits of a two-digit number is 12.
Then, x + y = 12. ...(i)
Required number = (10x + y).
Number obtained on reversing the digits = (10y + x).
As per given condition the number obtained by interchanging its digits exceeds the given number by 18.
{tex}\therefore{/tex} (10y + x) - (10x + y) = 18
{tex}\Rightarrow{/tex}10y + x - 10x - y = 18
{tex}\Rightarrow{/tex} 9y -9x = 18
{tex}\Rightarrow{/tex} y -x = 2. ...(ii)
On adding (i) and (ii), we get
(x + y) + (y -x) = 12 + 2
{tex}\Rightarrow{/tex} 2y = 14
{tex}\Rightarrow{/tex} y = 7.
Putting y = 7 in (i), we get
x + 7 = 12
{tex}\Rightarrow{/tex} x = 12 - 7 = 5
{tex}\therefore{/tex} x = 5 and y = 7.
Hence, the required number is 57.