If $$2xy^2 : 2x^2y :: 2x^2y : z$$​, which of the options below gives an expression equivalent to z?

Correct option is A

Given: ​

​$$2xy^2 : 2x^2y :: 2x^2y : z$$ 

Solution: ​

​$$2xy^2 : 2x^2y :: 2x^2y : z \\ \ \\ \frac{ 2xy^2} { 2x^2y} = \frac{2x^2y} z \\ \ \\ \implies z = \frac{2x^2y \times 2x^2 y }{2xy^2} \\ \ \\ z = 2x^3$$​​