You seem to be dealing with record oriented data where records are separated by empty lines. Often it is convenient to read a record as a time. Consider:

use strict;
use warnings;

my $data = <<DATA;
this is test only 1
Baki: 9.70

this is test only 2
Baki : 9.30

this is test only 3
Baki : 9.00
DATA

my $lastRecord;

open my $in, '<', \$data;

local $/ = "\n\n"; # Read a record at a time

while (defined (my $record = <$in>)) {
    chomp $record;
    next if $record =~ /$(?:Baki)/;
    $lastRecord = $record;
}

print $lastRecord;
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Prints:

this is test only 3
Baki : 9.00
[download]

Note the use of three parameter open and a lexical file handle. Usually there would be an or die ...; for the open as well, but in this case (using a string as a file) there is no need.