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

Given,

First : Second $=2:3$

Second : Third $=5:8$

Make the second term common.

LCM of $3$ and $5$ is $15$.

So,

First : Second $=10:15$

Second : Third $=15:24$

Therefore,

First : Second : Third $=10:15:24$

Sum of ratios:

$10+15+24=49$

Given sum of numbers is $98$.

So, one part is:

$\frac{98}{49}=2$

Second number is:

$15\times 2=30$