Please find an immediate solution below that's zero percent flexible.
Disadvantage: Need to write as many MAX(CASE WHEN =...) as to distinct username. Not flexible if userNames are more than 10, or can have more UserNames in future.
The right solution would be to redesign table and/or data entry.
SELECT
[Date]
, MAX(CASE WHEN UserName = 'Bubai' THEN TimeLogged END) AS [Bubai]
, MAX(CASE WHEN UserName = 'Bhanu' THEN TimeLogged END) AS [Bhanu]
, SUM(TimeLogged) AS Total
FROM [YourTable]
GROUP BY [Date]
For testing use this too:
SELECT
[Date]
, MAX(CASE WHEN UserName = 'Bubai' THEN TimeLogged END) AS [Bubai]
, MAX(CASE WHEN UserName = 'Bhanu' THEN TimeLogged END) AS [Bhanu]
, SUM(TimeLogged) AS Total
FROM
(
SELECT 1 as ID, '10/8/2012' as Date, 5.50 as TimeLogged, 'Bubai' AS UserName
UNION ALL
SELECT 2 as ID, '11/8/2012' as Date, 2.30 as TimeLogged, 'Bubai' AS UserName
UNION ALL
SELECT 3 as ID, '10/8/2012' as Date, 3.30 as TimeLogged, 'Bhanu' AS UserName
UNION ALL
SELECT 4 as ID, '11/8/2012' as Date, 7.30 as TimeLogged, 'Bhanu' AS UserName
)AS X
GROUP BY [Date]