Deoxyribonucleic Acid Computing (DNA) is a new computing technique. In this technique, the information is stored in DNA molecules and computational tool is available in the form of biochemistry operations. Computations are forming on string in DNA strand to produce results. In computer science, different models of DNA computing are available, in which some are equivalent to a classic Turing Machine. The researchers worked on improving error rates in this technique. Work is also found in different types of bio-operations used in this technique. The molecular engineering technique is studied by many researchers and found that this computation technique has a huge storage capacity. Limited work has been found that the researchers also tried to solve real-life applications by using this technique and tried to find the practical feasibility of DNA computers, (For example to break Data Encryption Standard (DES), to solve NP-complete and hard computational problems). In this study, different techniques have been studied for solving Path Problems using DNA computing and found the best technique by comparison. Also devised a new technique to solve the given path problems.