Lookup within a vlookup

I have a spreadsheet that has data for many different days and listed for each day is 12 rows of data. I need to be able to look up a date in column A and then lookup the last data entered in column C for that day. I also need to be able to return the time in column B that the last data was entered. I have attached a sample sheet.

Thanks

Based on your sample file, one approach:

L5: =LOOKUP(9.99E+307,OFFSET($C$1,MATCH($L$3,$A:$A,0)-1,,12,1))

L7: =MOD(LOOKUP(9.99E+307,OFFSET($C$1,MATCH($L$3,$A:$A,0)-1,,12,1),OFFSET($B$1,MATCH($L$3,$A:$A,0)-1,,12,1)),1)
format as hh:mm

both of the above are volatile by virtue of OFFSET - you could use INDEX as an alternative (to avoid Volatility) but the syntax would be quite a bit longer.