Question

If you reverse the digits of my mother's age, you get my father's age. And the sum of their ages is 11 times the difference between their ages. If my mother is younger than my father, how old is she?

Answer 1

Let your mother's age is xy = y + 10x
A/C to question,
if I reverse your mother's age , I get your father's age
means , father's age = yx = x + 10y

Again, said sum of their ages is 11 times the difference between their ages
e g., (y + 10x) + (x + 10y) = 11{(y + 10x) - (x + 10y)}
⇒11y + 11x = 11{9x - 9y }
⇒x + y = 9x - 9y
⇒-8x = -10y
⇒4x = 5y
x/y = 4 : 5
Let x = 4 then y = 5
∴ your mother's age = 5 + 10 × 4 = 45 yr
father's age = 4 + 10 × 5 = 54 yr