Question

Karen is 8 years old and Kate is 9 years old. What will Kate's age be when the total of the digits in both their ages is 17?

Answer 1

let it be x years from now

8+x + 9+x
= 2x + 17

x -Karen-Kate-sum of their ages- sum of digits of that
0 - 8 ----- 9 --- 17----------- 8
1 - 9 ------10 -- 19-----------10
2 - 10 -----11 -- 21-----------3
3 - 11 -----12 -- 23 -----------5
...
36 - 44 ----45 -- 89 -----------17

When Karen is 44
and Kate is 45
sum of their ages is 89
sum of the digits in both their ages is 17