SSC CHSL 9 Jan 2017 Shift 3 Paper

Let speed of Rajdhani train = x km/hr and Express train = y km/hr
Using, time = distance/speed
Acc. to ques, ⇒ $\frac{612}{\mathit{y}}-\frac{612}{\mathit{x}}=9$
⇒ $\frac{1}{\mathit{y}}-\frac{1}{\mathit{x}}=\frac{9}{612}=\frac{1}{68}$ ----(i)
If speed of express train is doubled = 2y km/hr
⇒ $\frac{612}{\mathit{x}}-\frac{612}{2\mathit{y}}=3$
⇒ $\frac{1}{\mathit{x}}-\frac{1}{2\mathit{y}}=\frac{3}{612}=\frac{1}{204}$ ----(ii)
Adding equations (i) and (ii), we get :
⇒ $\frac{1}{\mathit{y}}-\frac{1}{2\mathit{y}}=\frac{1}{68}+\frac{1}{204}$
⇒ $\frac{1}{2\mathit{y}}=\frac{4}{204}$
⇒ $\mathit{y}=\frac{102}{4}=\frac{51}{2}$ km/hr
∴ Speed of Rajdhani = $\frac{1}{\mathit{x}}=\frac{2}{51}-\frac{1}{68}$
⇒ $\frac{1}{\mathit{x}}=\frac{1}{17}\times \frac{5}{12}$
⇒ $\mathit{x}=\frac{204}{5}=40.8$ km/hr