A very effective spot spray for ragwort is - about 20% white distilled vinegar, a good dollop of salt, and good squeeze of washing up liquid, in water. I think the vinegar is the essential ingredient and the salt and washing up liquid just help, so you can experiment with them for quantity.
Anyway, spray the ragwort on a warm day when plants are dry and they will be withered by next day.
It will affect the grass as well, but not usually kill it where you get overspray, as the grass leaves have less surface area for uptake.