Reversing the digits makes the difference a multiple of 9 and the total a multiple of 11. For the difference to be an eleventh of the total, the two digits have to differ by 1 and add up to 9. That’s 4 and 5, so 45 and 54.
A woman says: “My husband’s age is my age with the digits reversed. He’s older than me, and the difference between our ages is an eleventh of the two added together.” How old are they?
Give me a hintThe hint
Reverse any two-digit number and the difference is always a multiple of 9.
Reveal the answerHide the answer
He’s 54 and she’s 45
Source: Henry Dudeney, Amusements in Mathematics, 1917, No. 41