I read this in the late 1970s or early 1980s, possibly as part of a juvenile fiction anthology/collection. From what I remember in this story a post-apocalyptic society requires each member to go out before their 18th birthday and kill an "oldster" adult (i.e. I think over 30 similar to the time in Logan's Run) to make room for themselves. Otherwise they will be killed.
The kids actually cut off the hand of the victim which has a tattoo on it with the birthdate/age. In this case, the world has gotten to the point the person who kills the oldest person gets a "prize" of one more year of life beyond 30. Note, this is NOT Logan's run nor the novel upon which it is based.
The hero in this case finds an old man, the oldest he had ever seen (something like 45-50 I think) making wonderful sounds with a strange device. It was a piano.
He then confronts the old man
... but cannot bear to kill him. The old man takes pity on the boy and offers him his hand to take back so he can live. The boy asks if the old man will still be able to play the piano with just one hand. The old man smiles and says "Yes, but not as well. " Then, the boy decides to stay with the old man and risk becoming an outlaw so he can learn to play the piano.