  It is observed that in some money exchange operations, the applied $n$
-variable mean $M$ should be self reciprocally-conjugate, i.e. it should
satisfy the equality \[ M\left( x_{1},\ldots,x_{n}\right) M\left(
\frac{1}{x_{1}},\ldots,\frac{1}{x_{n}} \right) =1,\quad x_{1},\ldots,x_{n}>0.
\] The main result says that the only weighted quasiarithmetic mean satisfying
this condition is the weighet geometric mean.
