When you reverse the digits of the number 13, the number increases by 18. How many other two digit numbers increase by 18 when their digits are reversed?
Let the number be 10x + y.
Then, (10y+x)−(10x+y)=18
⇒9(y−x)=18⇒y−x=2
So, the possible pairs of (x,y) are -
(1,3),(2,4),(3,5),(4,6),(5,7),(6,8) and (7,9).
But we want the numbers other than 13. Thus, there are 6 possible numbers, i.e., 24,35,46,57,68,79.
So, total number of possible numbers are 6.