Question

My mother and I are the same age – only the numbers are reversed (21,12 for example)
Twelve years ago my mom was twice as old as me.
So how old is my mommy and how old am I?

Answer 1

Let the two digits in the ages be x and y. Your mother's age now is 10x + y. Yours is 10 y + x.

Twelve years ago,

10 x + y -12 = 2 (10 y +x-12)
10 x + y = 20y + 2x -12
19y = 8x + 12

Try integers 0 through 9 for y and see which gives an integer for x.
Only this combination works:
y = 4, x = 8

Current ages are 48 and 84.
Twelve years ago they were 36 and 72

Answer 2

mom's age -- 10x + y
daughter ---- 10y + x

10x + y -12 = 2(10y +x - 12)
8x -19y = -12

now both x and y are probably integers, and y has to be less than x
I tried y = 1,2,3,4 and
y = 4 worked
when y = 4, x = 8

so mom is now 84 and the daughter is 48

check :
12 years ago mom was 72
and the daughter was 36 , check!