$$\text{Total distance =900} \mathrm{~km}$$
$$\therefore
\mathrm{x}+\mathrm{y}=900 \ \ \ \ \ldots \ldots (i)$$
$$\text{Time
taken to travel by bus with a speed of 60} \mathrm{~km} /
\mathrm{hr}=[\mathrm{x} / 60] \mathrm{hr}$$
$$\text{Time
taken to travel by railway with a speed of 90} \mathrm{~km} /
\mathrm{hr}=[\mathrm{y} / 90] \mathrm{hr}$$
$$\text{Total
tlme taken for the complete Journey =13} \mathrm{hrs}$$
$$\therefore\dfrac{x}{60}+\dfrac{y}{90}=13$$
$$\Rightarrow
90 x+60 y=70200 \ \ \ \ldots . . . . (ii) $$
$$\textbf{Step 2: Solving given system of linear equations.}$$
$$\text{Now, multiplying by 90 throughout the eq. (i) and subtracting It eq. (II) from (1), we get}$$
$$90 x+90
y=81000$$
$$90 x+60
y=70200$$
$$30
\mathrm{y}=10800$$
$$\therefore
\mathrm{y}=\mathbf{3 6 0 \mathrm { km }}$$
$$\text{And,}$$
$$x=900-360=540 \mathrm{~km}$$