At $T(K)$ the equilibrium constants for the following two reactions are given below

$ 2 A(g) \rightleftharpoons B(g)+C(g) ; K_{1}=16 $

$ 2 B(g)+C(g) \rightleftharpoons 2 D(g) ; K_{2}=25 $

What is the value of equilibrium constant $(K)$ for the reaction given below at $T(K)$ ?

$ A(g)+\frac{1}{2} B(g) \rightleftharpoons D(g) $