The sum of three numbers is 280. If the ratio between the first and second numbers is 2 : 3 and the ratio between second and third numbers is 4 : 5, then find the second number.

$$\eqalign{ & \,\,\,{{\text{I}}^{{\text{st}}}}\,\,\,{\text{I}}{{\text{I}}^{{\text{nd}}}}\,\,\,{\text{II}}{{\text{I}}^{{\text{rd}}}} \cr & \,\,2\,\,:\,\,3 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,4\,\,:\,\,5 \cr & \overline {\,8\,:\,12\,:\,15\,} \cr & 35{\text{ unit}} \to {\text{280}} \cr & {\text{1 unit}} \to 8 \cr & 12\,{\text{unit}} \to 12 \times 8 = 96 \cr} $$