The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:

Let the three parts be A, B, C. Then,
A : B = 2 : 3 and B : C = 5 : 8
$$\eqalign{ & = \left( {5 \times \frac{3}{5}} \right):\left( {8 \times \frac{3}{5}} \right) = 3:\frac{{24}}{5} \cr & \Rightarrow A:B:C = 2:3:\frac{{24}}{5} = 10:15:24 \cr & \Rightarrow B = {98 \times \frac{{15}}{{49}}} = 30 \cr} $$