A set of records was to be keyed in by a certain number of clerks in 12 days. Had 4 more clerks been put on the same set, it would have been keyed in in 9 days. How many clerks were originally put on it?

With $n$ clerks the set is $12n$ clerk-days; with $n+4$ clerks it is $9(n+4)$ clerk-days. The set is the same size, so $12n=9n+36$, giving $3n=36$ and $n=12$. 16 is the enlarged group $n+4$, not the original one. 36 reads the line $3n=36$ straight off as the answer without the last division. 3 divides 36 by 12 instead of by 3, inverting the final step.