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 × the difference between their ages. If my mother is younger than my father, how old is she?

a) 27 years
b) 36 years
c) 45 years
d) 54 years

Answer 1

The mother's age can be determined by setting up an equation and solving for the digits of her age.

Step-by-step explanation:

To solve this problem, let's assume the mother's age is represented by AB, where A and B are the digits in her age. According to the given condition, if we reverse the digits, we get BA, which represents the father's age.

Since the mother is younger than the father, A < B.

Now, the sum of their ages is 11 times the difference between their ages. So, we can set up the equation AB + BA = 11(B - A). Solving this equation, we find that A = 4 and B = 5. Therefore, the mother's age is 45 years (option c).