Step 1: Write the two given ratios.
First to second is $A:B = 2:3$, and second to third is $B:C = 5:8$.
Step 2: Make the common term B equal.
In the first ratio $B=3$, in the second $B=5$. The LCM of 3 and 5 is 15, so scale each ratio to make $B=15$.
Step 3: Scale the first ratio.
Multiply $A:B = 2:3$ by 5 to get $A:B = 10:15$.
Step 4: Scale the second ratio.
Multiply $B:C = 5:8$ by 3 to get $B:C = 15:24$.
Step 5: Combine into one chain.
Now $A:B:C = 10:15:24$, so the total number of parts is $10+15+24 = 49$.
Step 6: Find the second number.
The actual sum is 98, so one part equals $98 \div 49 = 2$. The second number is 15 parts, giving $15 \times 2 = 30$.
\[ \boxed{30} \]