Please solve this question:

Dear Student, 
Solution)
$$\begin{gathered} Since the ratio (2s-p):(3t-p) is duplicate of 2s:3t \\ So, \\ \frac{2s}{3t}=(\frac{2s-p}{3t-p}{)}^2 \\ \Rightarrow 2s(3t-p{)}^2=3t(2s-p{)}^2 \\ \Rightarrow 2s(9t^2+p^2-6tp)=3t(4s^2+p^2-4sp) \\ \Rightarrow 18s{t}^2+2s{p}^2-12stp=12t{s}^2+3t{p}^2-12stp \\ \Rightarrow 18s{t}^2+2s{p}^2=12t{s}^2+3t{p}^2 \\ \Rightarrow 18s{t}^2-12t{s}^2=3t{p}^2-2s{p}^2 \\ \Rightarrow 6st(3t-2s)=p^2(3t-2s) \\ \Rightarrow p^2=6st \end{gathered}$$
Hence Option(a) is correct.
Regards!