SQL to divide one row by another row based on formula or rule.

With MySampleData (Date, Name, ID, Result )
AS
(
SELECT CONVERT(datetime,'3/18/2013') ,'A',1,5 UNION ALL
SELECT '3/18/2013','B',2,16 UNION ALL
SELECT '3/18/2013','C',3,21 UNION ALL
SELECT '3/18/2013','D',4,11 UNION ALL
SELECT '3/18/2013','E',5,45 UNION ALL
SELECT '3/18/2013','F',6,22 UNION ALL
SELECT '3/18/2013','G',7,5 UNION ALL
SELECT '3/19/2013','A',1,2 UNION ALL
SELECT '3/19/2013','B',2,7 UNION ALL
SELECT '3/19/2013','C',3,15 UNION ALL
SELECT '3/19/2013','D',4,9 UNION ALL
SELECT '3/19/2013','E',5,19 UNION ALL
SELECT '3/19/2013','F',6,12 UNION ALL
SELECT '3/19/2013','G',7,3
)

select * from MySampleData

declare @MySampleData table (Date datetime, Name char(1), ID int, Result DECIMAL(20,9))
insert @MySampleData
SELECT CONVERT(datetime,'3/18/2013') ,'A',1,5 UNION ALL
SELECT '3/18/2013','B',2,16 UNION ALL
SELECT '3/18/2013','C',3,21 UNION ALL
SELECT '3/18/2013','D',4,11 UNION ALL
SELECT '3/18/2013','E',5,45 UNION ALL
SELECT '3/18/2013','F',6,22 UNION ALL
SELECT '3/18/2013','G',7,5 UNION ALL
SELECT '3/19/2013','A',1,2 UNION ALL
SELECT '3/19/2013','B',2,7 UNION ALL
SELECT '3/19/2013','C',3,15 UNION ALL
SELECT '3/19/2013','D',4,9 UNION ALL
SELECT '3/19/2013','E',5,19 UNION ALL
SELECT '3/19/2013','F',6,12 UNION ALL
SELECT '3/19/2013','G',7,3

;WITH cte_dat
AS
(
SELECT *
,CASE WHEN Name IN ('B','A') THEN 'B/A'
WHEN Name IN ('D','C') THEN 'D/C'
WHEN Name IN ('E','G') THEN 'E-G'
ELSE NULL
END AS Formula
FROM @MySampleData
)
SELECT Formula
,Date
,CASE WHEN Formula = 'B/A' THEN
MAX(CASE WHEN Name = 'B' THEN Result ELSE NULL END)/MAX(CASE WHEN Name = 'A' THEN Result ELSE NULL END)
WHEN Formula = 'D/C' THEN
MAX(CASE WHEN Name = 'D' THEN Result ELSE NULL END)/MAX(CASE WHEN Name = 'C' THEN Result ELSE NULL END)
WHEN Formula = 'E-G' THEN
MAX(CASE WHEN Name = 'E' THEN Result ELSE NULL END)-MAX(CASE WHEN Name = 'G' THEN Result ELSE NULL END)
END AS Result
FROM cte_dat
WHERE Formula IS NOT NULL
GROUP BY Formula, Date
ORDER BY Date, Formula

Eugene Elutin (3/19/2013)

Most of OP output results do not match relevant formulas, eg:
B/A 3/19/2013 = 7/ 2 = 3.5 not 0.285714286!

Any way thank's to Lowell for data setup:

declare @MySampleData table (Date datetime, Name char(1), ID int, Result  DECIMAL(20,9))
insert @MySampleData
SELECT CONVERT(datetime,'3/18/2013') ,'A',1,5  UNION ALL
SELECT '3/18/2013','B',2,16  UNION ALL
SELECT '3/18/2013','C',3,21  UNION ALL
SELECT '3/18/2013','D',4,11  UNION ALL
SELECT '3/18/2013','E',5,45  UNION ALL
SELECT '3/18/2013','F',6,22  UNION ALL
SELECT '3/18/2013','G',7,5  UNION ALL
SELECT '3/19/2013','A',1,2  UNION ALL
SELECT '3/19/2013','B',2,7  UNION ALL
SELECT '3/19/2013','C',3,15  UNION ALL
SELECT '3/19/2013','D',4,9  UNION ALL
SELECT '3/19/2013','E',5,19  UNION ALL
SELECT '3/19/2013','F',6,12  UNION ALL
SELECT '3/19/2013','G',7,3

;WITH cte_dat
AS
(
    SELECT  *
           ,CASE WHEN Name IN ('B','A') THEN 'B/A' 
                WHEN Name IN ('D','C') THEN 'D/C' 
                WHEN Name IN ('E','G') THEN 'E-G' 
                ELSE NULL
            END AS Formula
    FROM @MySampleData
)
SELECT   Formula
        ,Date
        ,CASE WHEN Formula = 'B/A' THEN
              MAX(CASE WHEN Name = 'B' THEN Result ELSE NULL END)/MAX(CASE WHEN Name = 'A' THEN Result ELSE NULL END)
              WHEN Formula = 'D/C' THEN
              MAX(CASE WHEN Name = 'D' THEN Result ELSE NULL END)/MAX(CASE WHEN Name = 'C' THEN Result ELSE NULL END)
              WHEN Formula = 'E-G' THEN
              MAX(CASE WHEN Name = 'E' THEN Result ELSE NULL END)-MAX(CASE WHEN Name = 'G' THEN Result ELSE NULL END)
        END   AS Result  
FROM cte_dat
WHERE Formula IS NOT NULL
GROUP BY Formula, Date
ORDER BY Date, Formula