In short, a ($\mathbb{C}P^n\sharp\mathbb{C}P^n$)-bundle type quasitoric manifold is an iterated ($\mathbb{C}P^n\sharp\mathbb{C}P^n$)-bundle over a point equipped with a good torus action. If $n=2$, then any graded ring isomorphism in integral cohomology is realized as a weakly equivariant homeomorphism. The higher dimensional analogue of this theorem deos not hold, but we can show that any isomorphism between the cohomology rings of ($\mathbb{C}P^n\sharp\mathbb{C}P^n$)-bundle type quasitoric manifolds preserves their Pontrjagin classes.