What is the quickest& most thorough way to clean the grout on my tile?

I don't know where you live, but in Florida, there is a company called Groutsmith. I had them come to my house to explain what would be done. Then he did a demo. I was blown away! And the price to do all 5 of my rooms with tile and filthy grout was based on square footage, so pricing varies by total square feet, but in was $340 with a 10 year guarantee! I also bought 2 bottles of the cleaner. It's no big deal, but it was handy to have on hand and you only need a microfiber mop.

Now, if ketchup is spilled on tole and grout, I just wipe it up and there is no stain on the grout.

Floor tile? I use Oxi Clean powder (you can be generous) mixed with hot water & spray it on the grout & tiles. Let sit for a few minutes & scrub with a stiff brush. Worked magic on my tiles!

The best way I know how is to use a toothbrush and some watered down bleach.

I used vinegar and baking soda with a toothbrush. Brush it on. Let it set. Rinse. It wasn't fast but it was effective.

http://www.hometalk.com/search/posts?filter=clean%20grout

Oh, shoot! I'm going to think about this and research it and get back with you if I find any information. Sorry I was of no help!