"As a retired math teacher, I can tell you that by reversing the digits representing my current age and increasing the result by 13 you get my age reduced by 50%."
How old is she?
Let the teacher's age be given by: 10x+y
Then, by the given conditions, we must have:
10y+x+13 = (10x+y)/2
=> 20y -y +26 = 10x-2x
=> 8x -19 y =26
=> 8x == 7 ( mod 19)== 64 (mod 19)
=> x == 8(mod 19)
Since, x=8, this gives:
8 *8 -19y = 26
Or, 19y = 64-26=38
or, y = 2
or, (x, y) = (8,2)
Therefore, the required age of the teacher is 82.
Puzzle Solution
