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This question has probably been asked a million times but our toilet has begun running after it's flushed. I give the handle the usual quick push & it stops.
Tired of waiting around to see if it's going to stop running.
When our toilet did that we had to buy a new ball cock. As its that
which controls the water flow. It does break every now and again
and once you have got a new one put in the flow should be OK.
Without seeing it and assuming that it is not over filling which it doesn't sound like then replacing the outlet valve (basically just a piece of rubber) should fix it. (and assuming it is not a cistern out of the ark).
That and the inlet valve are the most common/likely problem with a modern cistern.
A visit to the local hardware plumbing section with the model of your cistern should solve that problem - it is very easy to do.