How to take grade letter from marks range from grade table? Grade Table is: 

create table Grade 
{
grade_letter char(1)
lowerlimit int(20)
upperlimit int(20)
};

insert into Grade (grade_letter, lowerlimit, upperlimit) 
    values (
      ('A', 85, 100),
      ('B', 70,  84),
      ('C', 50,  69),
      ('F',  0,  49));


Suppose some another query returns marks.

Now, I am stuck with the query which takes the grade_letter based on the marks falling in the range given above. I want a query which is not hard-coded and calculates the grade based on the values given in the table only.
This will do the trick (assuming your marks are in the table Marks):

SELECT      B.grade_letter
FROM        Marks AS A
INNER JOIN  Grade AS B
    ON      A.Mark BETWEEN B.lowerlimit AND B.upperlimit