$A$ says to $B$: »I will tell you how old you are if you answer the following question. Multiply the digit in the tens place of your birth year by 5, add 2 to this product, and then multiply the resulting sum by 2. Add the units digit of your birth year to this new product and tell me the number you get!«

$B$ replies: »43«, whereupon $A$ immediately exclaims: »You are 16 years old!« How did $A$ know this?
Let the last two digits of the birth year be $x$ and $y$. B performs the following operations:

$$
(5 x+2) \cdot 2+y=10 x+y+4=43
$$

$10 x+y$ is nothing but the part of the birth year that exceeds 1900 (or 1800). We see that exactly 4 needs to be added to this to get the number stated (here 43). Therefore, 4 must be subtracted from the stated number to get the last two digits of the birth year; in this case, $43-4=39$. Thus, the birth year is 1939 (or 1839); subtracting this from the current year (1955), we get the person's age: 16 (or 116) years. (This ambiguity should not cause confusion, as we can immediately see whether someone is 16 or 116 years old when facing them.)

Gelencsér Júlia (Kiskunhalas, Szilády Á. g. I. o. t.)