When we reverse the digits of the number 13, the increases by 18. How many other two digit numbers increases by 18 when their digits are reversed?

Solution (By Examveda Team)

Let the numbers are in the form of (10x + y), so when the digits of the number are reversed the number becomes (10y + x)
According to question,
(10y + x) - (10x + y) = 18
Or, 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 need the number other than 13.
Thus, there are 6 possible numbers i.e. 24, 35, 46, 57, 68, 79
So, total numbers of possible numbers are 6