If two rods of length L and 2L having coefficients of linear expansion $\;\alpha\;$ & $\;2 \alpha\;$ respectively are connected such that length becomes 3L ,The average coefficient of linear expansion of the composite rod equals ---

Question

$(a)\;1.5\;\alpha\qquad(b)\;(\large\frac{5}{3})\;\alpha\qquad(c)\;1.25\;\alpha\qquad(d)\;(\large\frac{7}{5})\;\alpha$