Step 1: Understand aminoacyl tRNA synthetases.
Aminoacyl tRNA synthetases are enzymes responsible for attaching the correct amino acid to its corresponding tRNA molecule during protein synthesis. This process is called tRNA charging.
Step 2: Recall the number of amino acids.
In the standard genetic code, proteins are synthesized using \(20\) standard amino acids.
Step 3: Understand codon degeneracy.
Although there are \(61\) sense codons coding for amino acids, many codons specify the same amino acid. This phenomenon is known as degeneracy of the genetic code.
Step 4: Relation between synthetases and amino acids.
Each amino acid generally has its own specific aminoacyl tRNA synthetase enzyme that recognizes both the amino acid and the appropriate tRNA molecules.
Step 5: Count the required enzymes.
Since there are \(20\) amino acids, one specific synthetase is needed for each amino acid.
\[
20 \text{ amino acids } \Rightarrow 20 \text{ aminoacyl tRNA synthetases}
\]
Step 6: Analyze the incorrect options.
\(61\) and \(64\) correspond to codons, not synthetases.
\(40\) is not biologically associated with the number of aminoacyl tRNA synthetases.
Step 7: Final conclusion.
Therefore, the number of aminoacyl tRNA synthetases required is
\[
\boxed{20}
\]
Hence, the correct answer is option (D).