Try this

#!/usr/local/bin/perl
open (INFILE1, "/home/ashokpj/merge1.txt") ||
     die ("Cannot open input file merge1\n");
open (INFILE2, "/home/ashokpj/merge2.txt") ||
     die ("Cannot open input file merge2\n");
open (INFILE3, "/home/ashokpj/merge3.txt") ||
     die ("Cannot open input file merge2\n");

chomp($line1 = <INFILE1>);
chomp($line2 = <INFILE2>);
chomp($line3 = <INFILE3>);
while ($line1 ne "" || $line2 ne "" || $line3 ne "" ) {
print  $line1.$line2.$line3."\n";
if ($line1 ne "") {
   chomp($line1 = <INFILE1>);
}
if ($line2 ne "") {
   chomp($line2 = <INFILE2>);
}
if ($line3 ne "") {
   chomp($line3 = <INFILE3>);
}

}
close(INFILE1);
close(INFILE2);
close(INFILE3);
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