A. Gray presented an interesting O (n) invariant decomposition of the covariant derivative of the Ricci tensor. Manifolds whose Ricci tensor satisfies the defining property of each orthogonal class are called Einstein-like manifolds. In the present paper, we answered the following question: Under what condition(s), does a factor manifold M i , i = 1, 2 of a doubly warped product manifold M = f 2 M 1 × f 1 M 2 lie in the same Einstein-like class of M? By imposing sufficient and necessary conditions on the warping functions, an inheritance property of each class is proved. As an application, Einstein-like doubly warped product space-times of type A, B or P are considered