--I have two tables with no common columns: 
declare @Graph_Range table (Start_Range decimal(3,2), End_Range decimal(3,2))
insert @Graph_Range
select 0.10, 0.20 union all
select 0.20, 0.30 union all
select 0.30, 0.40 

declare @Graph_data table (Asset int, factor decimal(3,2), [case] int)
insert @Graph_data
select 500, 0.12, 1 union all
select 270, 0.13, 2 union all
select 300, 0.27, 3 union all
select 240, 0.23, 4 union all
select 200, 0.13, 5 union all
select 100, 0.12, 6 


--I need results as Lower Limit Upper Limit Sum_Asset 
--0.10 0.20 1,070 
--0.20 0.30 540 
--0.30 0.40 - 

--i.e. it should give sum of asset values in case the relevant factor falls between start and end range. 
select
Start_Range, 
End_Range, 
SUM(Asset) as Sum_Asset
from
(
 SELECT 
 A.Start_Range, 
 A.End_Range, 
 B.Factor,
 B.Asset
 FROM @Graph_Range AS A 
 LEFT JOIN @Graph_Data AS B ON B.Factor between A.Start_Range and A.End_Range
)dt
GROUP BY Start_Range, End_Range

SELECT g.Start_Range AS Lower_Limit,
g.End_Range AS Upper_limit,
COALESCE(d.SumAsset,0) AS Sum_Asset
FROM Graph_Range g
OUTER APPLY (SELECT SUM(Asset) AS Sum_Asset 
             FROM Graph_data 
             WHERE factor BETWEEN g.Start_Range AND g.End_Range 
            )d