$a,x,y,z,b$ are in AP such that $x+y+z=15$ and $a$, $\alpha$, $\beta$, $y$, $b$ are in HP such that $\large\frac{1}{\alpha}+\large\frac{1}{\beta}+\large\frac{1}{\gamma}=\large\frac{5}{3}$. Find $a$, $(a > b)$.

Question

$(a)\;9\qquad(b)\;1\qquad(c)\;\large\frac{1}{9}\qquad(d)\;5$