I have been debating with my girlfriend over this. She says, Supergirl is younger than Superman. I say, nope.
According to her, Supergirl wasn't born when Krypton was destroyed. She was born on Agro City which survived Krypton's destruction.
Kara Zor-El is the last survivor of Argo City, which had survived the explosion of the planet Krypton and drifted through space. When the inhabitants of the colony are slain by Green Kryptonite, which was released by meteorites striking the lead barrier, Kara is sent to Earth by her father Zor-El to be raised by her cousin Kal-El (Superman).
Zor-El was seeking Superman to raise Supergirl, so my girlfriend says that she won. I say the concern might be because she was a girl (but I am not confident.)
I have seen Supergirl try taking responsibility of her baby cousin. She has even said it exclusively that She doesn't like a Kryptonian half her age flying into danger. I have seen it many times, so I am confused. Does she say such things humorously or she is older than Superman?