Question

I have a friend Monty who became a magician more than 45 years ago, shortly after his son Vic was born. Monty the Magician told me that his and Vic’s ages are numerically reverses. Vic is 27 years younger than his father. How old is Monty the Magician

Answer 1

• Vic: 47
• Monty: 74

Explanation:

Reversing the digits of a 2-digit number changes its value by a factor of 9 times the difference of the digits. Here, the value is changed by 27, so the digits of the two ages differ by 27/9 = 3.

If Vic is slightly more than 45 years old, he would need to be 47 to have the digits of his age differ by 3.

Vic is 47

Monty is 74

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Maybe you want to see how that digit reversal thing works. Suppose xy is 2-digit number with x being the 10s digit and y being the 1s digit. Its value is then ...

10x +y

Reversing the digits changes the value to ...

10y +x

The difference in the two values is then ...

(10x +y) -(10y +x) = 9x -9y = 9(x -y)