To solve this problem, we need to identify the purines found in both DNA and RNA. Let's analyze the options:$\newline \bullet$Purines are a type of nitrogenous base found in nucleic acids. The two purines are adenine and guanine.$\newline \bullet$In DNA, the nitrogenous bases include adenine, guanine, cytosine, and thymine.$\newline \bullet$In RNA, the nitrogenous bases include adenine, guanine, cytosine, and uracil.$\newline \bullet$Therefore, the purines common to both DNA and RNA are adenine and guanine.$\newline$Now, let's evaluate the options:$\newline \bullet$Option 1: Adenine and Thymine - Thymine is not a purine; it is a pyrimidine.$\newline \bullet$Option 2: Adenine and Guanine - Both are purines and are found in both DNA and RNA.$\newline \bullet$Option 3: Guanine and Cytosine - Cytosine is a pyrimidine, not a purine.$\newline \bullet$Option 4: Cytosine and Thymine - Both are pyrimidines, not purines.$\newline$Therefore, the correct option is Option 2: Adenine and Guanine.