SSC CHSL 7 Jan 2017 Shift 1 Paper

Let speed of Rajdhani train = x km/hr and Express train = y km/hr
Using, time = distance/speed
Acc. to ques, ⇒ $\frac{816}{\mathit{y}}-\frac{816}{\mathit{x}}=9$
⇒ $\frac{1}{\mathit{y}}-\frac{1}{\mathit{x}}=\frac{9}{816}=\frac{3}{272}$ -----(i)
If speed of express train is doubled = 2y km/hr
⇒ $\frac{816}{\mathit{x}}-\frac{816}{2\mathit{y}}=4$
⇒ $\frac{1}{\mathit{x}}-\frac{1}{2\mathit{y}}=\frac{4}{816}=\frac{1}{204}$ -----(ii)
Adding equations (i) and (ii), we get :
⇒ $\frac{1}{\mathit{y}}-\frac{1}{2\mathit{y}}=\frac{3}{272}+\frac{1}{204}$
⇒ $\frac{1}{2\mathit{y}}=\frac{9+4}{816}$
⇒ $\mathit{y}=\frac{408}{13}$ km/hr
∴ Speed of Radhani = $\frac{1}{\mathit{x}}=\frac{13}{408}-\frac{3}{272}$
⇒ $\frac{1}{\mathit{x}}=\frac{26-9}{816}=\frac{17}{816}$
⇒ $\mathit{x}=\frac{816}{17}=$ 48 km/hr