If you don't need the exact Rank semantics (i.e. tied ranks). You can use the index available with select projections
var rank = data.GroupBy(d => d.CategoryKey)
.SelectMany(g => g.OrderByDescending(y => y.Rate * @BAES_RATE)
.Select((x,i) => new{g.Key, Item=x, Rank=i+1}))
Otherwise you can look at this answer