Question 637479
Let m = Mom's age = ab
Let d = Dad's age = ba > ab
Numerically  (assuming Dad < 100 years old)
m = 10a + b
d = 10b + a
Then 
m + d = 10a + b + 10b +a = 11a + 11b = 11*(a+b)
d - m = (10b + a) - (10a + b) = 9b - 9a = 9*(b - a)
Since m+d = 11*(d-m) we have
11*(a+b) = 11*9*(b-a) or
(a+b) = 9*(b-a)
This is satisfied when
(a+b) = 9
(b-a) = 1
Solving this pair of equations for a and b yields
a = 4
b = 5
Therefore the Dad is 54 and Mom is 45.
Are they correct? Let's see.
Is 45 the reverse of 54? Yes
Is [(45+54) = 11*(54-45)]?
Is [99 = 11*9]?
Is [99=99]? Yes