If the rest of your intervals are steps of 5 then a little math manipulation does most of the work.

my %num = (15=>1, 20=>2, 25=>3, 30=>4);

print $_, ' maps to ', $num{ ( 1 + int( ($_ - 1) / 5) ) * 5}, $/ for 1
+0 .. 31
10  maps to  Use of uninitialized value in print 
11  maps to  1
12  maps to  1
13  maps to  1
14  maps to  1
15  maps to  1
16  maps to  2
17  maps to  2
18  maps to  2
19  maps to  2
20  maps to  2
21  maps to  3
22  maps to  3
23  maps to  3
24  maps to  3
25  maps to  3
26  maps to  4
27  maps to  4
28  maps to  4
29  maps to  4
30  maps to  4
31  maps to  Use of uninitialized value in print
[download]

Then you only need if statements to catch those below a minimum or greater than the highest key.

Update The the light of the additional info you provided above, you could use this (if the size of the hash is fairly small).

for my $num (10,15,16,22,27,30,31) { 
    print $num, $num{
        ( 
            grep{ $_ >= $num } 
            sort{ $a <=> $b } keys %num 
        )[0]}, 
        $/; 
}
[download]

Again, you would need a conditional to cover those larger than the highest.

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