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