Aryan put $84$ red, $98$ yellow, and $72$ black colour $T-$shirts on sale. At the end of the day, he found $\frac{1}{4}$ of red T-shrits, $\frac{6}{7}$ of yellow T-shirts and $\frac{1}{12}$ of black T-shirts are left unsold. What fraction of the total T-shirts were left with him?
$(a)$ Multiply $\frac{1}{3}$ of $15$ by $3 \frac{1}{5}$.
$(b)$ Divide the product of $\frac{1}{2}$ and $15 \frac{1}{2}$ by the product of $\frac{1}{3}$ and $13 \frac{1}{2}$.