For 1 ≤ r ≤ n − 1, let Gr,n denote the Grassmannian parametrizing r -dimensional subspaces of Cn. Let (r, n) = 1. We show that the GIT quotients of certain Richardson varieties in Gr,n for the action of a maximal torus in SL(n, C) are the product of projective spaces with respect to the descent of a suitable line bundle.