(one) doesn't give a rip (about something) phrase
"A rip" is simply a euphemism, a more socially acceptable version of a stronger swear word.
If "one doesn't give a rip about something", that person emphasizes that he/she doesn't care about it.
I don't know what's bothering her now and I don't give a rip about it. She's always in a foul mood for no apparent reason.
Tim will sit for an exam on tomorrow's morning but he doesn't give a rip about doing revision.
Be outside the ability or willingness of someone to care more about a particular person or issue
How's it going?; how are you?
An individual should only work on and care about his or her work, and should not interfere with others.
To spend a lot of effort, time, and care on doing something.
The origin of the term is unclear.
Used to emphasize that someone or something is a lot more or a lot better
Mia can paint a damn sight better than I can.