A train runs past a telegraph pole in 15 s and through a tunnel of length 450 m in 45 s. The length of the train is

Time taken to cross the pole   =15s
time taken to cross the tunnel =45s
length of the tunnel  =450m
length of the train  =xm
$\begin{array}{r}{\mathrm{V}}_{\mathrm{avg}}=\frac{\mathrm{x}}{\mathrm{t}}{\mathrm{v}}_{\mathrm{avg}}=\frac{\mathrm{x}}{15}\end{array}$
$\begin{array}{r}\frac{\mathrm{x}}{15}=\frac{(\mathrm{x}+450)}{45}\Rightarrow 3\mathrm{x}=\mathrm{x}+450\\ \Rightarrow 2\mathrm{x}=450\Rightarrow \mathrm{x}=\frac{450}{2}=225\mathrm{m}\end{array}$