It is given that: The average of p and q is 20 \(\begin{align} & \therefore \dfrac{p+q}{2}=20 \\ & \Rightarrow p+q=40 \,\,\,\,\,\,\,\ ...\left( 1 \right) \\ \end{align}\) The average of q and y is 25. \(\begin{align} & \therefore \frac{q+y}{2}=25 \\ & \Rightarrow q+y=50\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( 2 \right) \\ \end{align}\) The average of p, q, and y is 23. \(\begin{align} & \therefore \dfrac{p+q+y}{3}=23 \\ & \Rightarrow p+q+y=69\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( 3 \right) \\ \end{align}\) By subtracting equation (2) from (3), we get \(\begin{align} & \therefore (p+q+y) - (q+y) = 69 - 50 \\ & \Rightarrow p=19 \\ \end{align}\) By subtracting equation (1) from (3), we get \(\begin{align} & \therefore (p+q+y) - (p+q)=69 - 40 \\ & \Rightarrow y=29 \\ \end{align}\) Now, the average of p and y. \(\therefore \dfrac{p+y}{2}=\dfrac{19+29}{2}=\dfrac{48}{2}=24\) Hence, the correct answer is "option 1".