Dispaly Results from left join takes lot of time - MSSQL I have the following query (just for example): 

SELECT
     a.id
    , a.name
FROM db.schema.tablea a
    LEFT JOIN db.schema.tableb b
        ON a.id = b.id    -- number
        AND a.name = b.name    --string


This query takes usually 1 second to run.

But, the following query takes 20 seconds to run:

SELECT
    a.id
    , a.name
    , b.value
FROM db.schema.tablea a
    LEFT JOIN db.schema.tableb b
        ON a.id = b.id    -- number
        AND a.name = b.name    --string


In other words, display the results (b.value) makes the query 20 times slower.
In my specific case, I make a left join on two columns: string (lenght max 10) and number. The result (b.value in my example) is a float.

The joined table has 3 columns and ca 2000 rows.
Perhaps you see a join elimination? We can't say since you didn't give us any details (like execution plan) and also your query is simplified, so we can't say whether join elimination is possible in the first place. Join elimination is when SQL Server determines that it doesn't have to access a table at all, so it eliminates it from the execution plan. Here's an example using Adventureworks where the is no need to access the referencing table (in a FK relationship) since we didn't pick any columns from it (note the commented column):

SELECT DISTINCT c.CustomerID, c.AccountNumber--, h.Freight 
FROM Sales.Customer AS c 
LEFT OUTER JOIN Sales.SalesOrderHeader AS h ON c.CustomerID = h.CustomerID


And here is a different example where it doesn't access the referenced table, since we preserve the referencing table and don't pick any columns from the referenced table:

SELECT h.Freight, h.CustomerID, h.CustomerID
FROM Sales.Customer AS c
RIGHT OUTER JOIN Sales.SalesOrderHeader AS h ON c.CustomerID = h.CustomerID