First, second, third

Suppose, the three numbers are $x, y$ and $z$ .

Sum of the numbers is $98$ .

Now,

$x + y + z = 98………………(1)$

The ratio of the first to the second is $\dfrac{2}{3}$

$\dfrac{x}{y}$ = $\dfrac{2}{3}$

$x =$ $\dfrac{2}{3}$ $\cdot$ $y$ .

$x =$ $\dfrac{2}{3}$

The ratio of the second to the third is $\dfrac{5}{8}$

$\dfrac{y}{z}$ $=$ $\dfrac{5}{8}$

$\dfrac{z}{y}$ $=$ $\dfrac{8}{5}$

$z =$ $\dfrac{8}{5}$ $\cdot$ $y$ .

$z =$ $\dfrac{8}{5}$

Put the value of $x =$ $\dfrac{2y}{3}$ and $z =$ $\dfrac{8y}{5}$ in $(1)$ .

$\dfrac{2y}{3}$ $+ y +$ $\dfrac{8y}{5}$ $= 98$

$\dfrac{49y}{15}$ $= 98$ .

$49y = 98 × 15$ .

$49y = 1470$ .

$y =$ $\dfrac{1470}{49}$ .

$y = 30$ .

Therefore, the second number is $30$ .