Include ID Field In GROUP BY Statement

I've got a query where i need to return a max value based on a select but one of the fields i need to return in the results is the records primary key ID No. This messes up the MAX bit and means that all results are returned, not just the max one.

 The query i'm using is very long so i've simplified what i mean by the example below. Say i have a table 'Fruits':

ID      FruitName      Cost
1       Apple             0.45
2       Apple             0.63
3       Apple             0.52
4       Pear              0.89
5       Pear             0.83

And run the query:

select max(Cost),FruitName From Fruits
group by FruitName

It'll correctly return:

FruitName      Cost
Apple             0.63
Pear              0.89

Now i need the ID also returned by my query so i go:

select max(Cost),FruitName,ID From Fruits
group by FruitName,ID

This doesnt return the above results with the ID appended to it, it instead returns:

ID      FruitName      Cost
1       Apple             0.45
2       Apple             0.63
3       Apple             0.52
4       Pear              0.89
5       Pear             0.83

As the ID is always distinct and therefore messes up the grouping. How in this instance would i return the correct result of:

ID      FruitName      Cost
2       Apple             0.63
4       Pear              0.89

 Thanks.