I mean ive washed off grout in a bathroom sink. But ive never poured an 80lbs bag down it with the tap on 🤷‍♂️ 

 You don't need a lot of concrete, just pour some cement in the sinks, leave the tap running until it goes through, close the tap, few hours later you have damaged the pipes beyond repair, they might work partially, but to fix you have to redo from sink to septic tank. If the house is cheap and old like the story implies then it's easier to build a new one.