Question

A woman says " if you reverse my own age the figure represents my husbands age, he is of course senior to me and the difference between our ages is one-eleventh of their sum ". The woman's age is:

• A. 24 years
• B. 34 years
• C. 45 years
• D. 35 years

Answer 1

Answer:

C. 45 years

Let the woman’s age be (10x + y) (so digits are (x) and (y)).
Then her husband’s age (reverse digits) is (10y + x).

Given condition 1:

Husband is older:
10y + x > 10x + y
\Rightarrow y > x

Given condition 2:

Difference between ages = one-eleventh of their sum

$(10y + x) - (10x + y) = \frac{1}{11}\big[(10y + x) + (10x + y)\big]$

Simplify:

Difference:
9(y - x)

Sum:
11(x + y)

So:
$9(y - x) = \frac{1}{11} \cdot 11(x + y)$
9(y - x) = x + y

Solve:

9y - 9x = x + y
9y - y = 9x + x
8y = 10x
4y = 5x

So:
x : y = 4 : 5

Thus:
$x = 4,\quad y = 5$

Woman’s age:

10x + y = 10(4) + 5 = 45
Final Answer:

$\boxed{45 \text{ years}}$