You could do this by maintaining an array in which you keep incrementing the various fields as you read lines. Like so:

use strict;

my @data;
open(INPUT,'<',"monks.dat") or die("Can't open file");
while (<INPUT>) {
    chomp;
    my @newdata = split(/ +/);
    for my $index (0 .. $#newdata) {
        $data[$index] += $newdata[$index];
    }
}
close(INPUT);
[download]

Though this does not check whether the amount of fields is actually the same or not :)