A person buys tea of three different qualities at ₹$ \; 800,$ ₹ $\; 500,$ and ₹$ \; 300 \; \text{per kg},$ respectively, and the amounts bought are in the proportion $2:3:5.$ She mixes all the tea and sells one-sixth of the mixture at ₹$ \; 700 \; \text{per kg}.$ The price, in $\text{INR per kg},$ at which she should sell the remaining tea, to make an overall profit of $50 \%,$ is

- $675$
- $653$
- $692$
- $688$