The sum of the digits of a two digit number is 12. The number obtained by reversing its digits exceeds the given number by 18. Then the number is______

Let the one's digit and ten's digt be x and y respectively.

From the given conditions, we have:

 

x + y = 12

10y + x + 18 = 10x + y   or   9y - 9x + 18 = 0  or  y - x = -2

 

Adding the above two equations, we get,

2y = 10

y = 5

 

So, x = 12 - 5 = 7

 

Thus, the required number is 57.