[tex]\large\underline{\sf{Solution-}}[/tex]

Let assume that

First number = x

Second number = y

Third number = z

Given that,

The ratio of first to the second number is 2:3

[tex]\sf \: x : y \: = \: 2 : 3 \\ [/tex]

[tex]\sf \: \dfrac{x}{y} = \dfrac{2}{3} \\ [/tex]

[tex]\sf \: \sf \: \implies \: x = \dfrac{2y}{3} - - - - (1) \\ \\ [/tex]

Further, given that

The ratio of second to third is 5:8

[tex]\sf \: y : z \: = \: 5 : 8 \\ [/tex]

[tex]\sf \: \dfrac{y}{z} = \dfrac{5}{8} \\ [/tex]

[tex]\sf \: \sf \: \implies \: z = \dfrac{8y}{5} - - - - (2) \\ \\ [/tex]

Further given that, rhe sum of the three numbers is 98.

[tex]\sf \: x + y + z = 98 \\ [/tex]

[tex]\sf \: \dfrac{2y}{3} + y + \dfrac{8y}{5} = 98 \\ [/tex]

[tex]\sf \: \dfrac{10y + 15y + 24y}{15} = 98 \\ [/tex]

[tex]\sf \: \dfrac{49y}{15} = 98 \\ [/tex]

[tex]\sf \: y = 2 \times 15 \\ [/tex]

[tex]\bf\implies \:y = 30 \\ \\ [/tex]

Hence, Second number is 30.