The problem is a defective diaphram in the fill valve. You could dissassemble and replace the diaphrame, but if you have an older brass bodied fill valve often they are very difficult to open, and may have a problem finding repair parts to fit it.
The option is to replace the fill valve, which is really a simple and inexpensive project. You can get a universal repair fill valve at any hardware store or home supply for about $10 and install it yourself in about 15 to 30 minutes.
I personally prefer those made by fluidmaster, but there are other ones available. If you already have a fluidmaster valve you can get a replacement diaphram for it at any hardware for about $2.
to replace the diaphrame, turn the water off, pull the top off the valve and lift the inner section up and out. Remove the diaphram and insert the new one, then replace the top top part of the valve, turn the water on and your done.
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