SSC CPO SI and ASI Model Paper 6

(4) In such types of questionswhere two trains start towards eachother and cross each other to reachtheir respective destinations, thereis a relation between the speed andtime of the two trains (trains A andB in this case), i.e.
$\frac{\mathit{S}\mathit{p}\mathit{e}\mathit{e}\mathit{d}\mathit{o}\mathit{f}\mathit{t}\mathit{r}\mathit{a}\mathit{i}\mathit{n}\mathit{A}}{\mathit{S}\mathit{p}\mathit{e}\mathit{e}\mathit{d}\mathit{o}\mathit{f}\mathit{t}\mathit{r}\mathit{a}\mathit{i}\mathit{n}\mathit{B}}=\sqrt{\frac{\mathit{T}\mathit{i}\mathit{m}\mathit{e}\mathit{t}\mathit{a}\mathit{k}\mathit{e}\mathit{n}\mathit{b}\mathit{y}\mathit{t}\mathit{a}\mathit{i}\mathit{n}\mathit{B}}{\mathit{T}\mathit{i}\mathit{m}\mathit{e}\mathit{t}\mathit{a}\mathit{k}\mathit{e}\mathit{n}\mathit{b}\mathit{y}\mathit{T}\mathit{r}\mathit{a}\mathit{i}\mathit{n}\mathit{A}}}$Thus,
Let the speed of Train A = ${\mathit{S}}_{\mathit{A}}$, and
the time taken by Train $\mathit{A}=5\frac{1}{7}$hSpeed of Train B = 54 km/h, andthe time taken by Train B = $9\frac{1}{7}$ h
$\frac{{\mathit{s}}_{\mathit{A}}}{54}=\sqrt{\frac{\frac{64}{7}}{\frac{36}{7}}}=\sqrt{\frac{64\times 7}{7\times 36}}=\frac{8}{6}$
${\mathit{s}}_{\mathit{A}}=\frac{8\times 54}{6}=72$km/h