Let $r$ and $q$ be positive integers and $n=qr+1.$ Let $G = SL(n, \mathbb{C})$ and $T$ be a maximal torus of $G.$ Let $P^{α_r}$ be the maximal parabolic subgroup of $G$ corresponding to the simple root $α_r.$ Let $ω_r$ be the fundamental weight corresponding to $α_r.$ Let $W$ be the Weyl group of $G$ and $W_{P^{α_r}}$ be the Weyl group of $P^{α_r}.$ Let $W^{P^{α_r}}$ be the set of all minimal coset representatives of $W/W_{P^{α_r}}$ in $W.$ Let $w_{r,n}$ (respectively, $v_{r,n}$) be the minimal (respectively, maximal) element in $W^{P^{α_{r}}}$ such that $w_{r,n}(nω_r) \leq 0$ (respectively, $v_{r,n}(nω_r) \geq 0$). Let $v \leq v_{r,n}$ and $X^v_{w_{r,n}}$ be the Richardson variety in $G_{r,n}$ corresponding to $v$ and $w_{r,n}.$ In this article, we give a sufficient condition on $v$ such that the GIT quotient of $X^{v}_{w_{r,n}}$ for the action of $T$ is the product of projective spaces with respect to the descent of the line bundle $\mathcal{L}(nω_r).$