SSC CHSL 10 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, ⇒ $\frac{780}{\mathit{y}}-\frac{780}{\mathit{x}}=8$
⇒ $\frac{1}{\mathit{y}}-\frac{1}{\mathit{x}}=\frac{8}{780}=\frac{2}{195}$ ------(i)
If speed of express train is doubled = 2y km/hr
⇒ $\frac{780}{\mathit{x}}-\frac{780}{2\mathit{y}}=6$
⇒ $\frac{1}{\mathit{x}}-\frac{1}{2\mathit{y}}=\frac{6}{780}=\frac{1}{130}$ ------(ii)
Adding equations (i) and (ii), we get :
⇒ $\frac{1}{\mathit{y}}-\frac{1}{2\mathit{y}}=\frac{2}{195}+\frac{1}{130}$
⇒ $\frac{1}{2\mathit{y}}=\frac{4+3}{390}=\frac{7}{390}$
⇒ $\mathit{y}=\frac{195}{7}$ km/hr
∴ Speed of Rajdhani = $\frac{1}{\mathit{x}}=\frac{7}{195}-\frac{2}{195}$
⇒ $\frac{1}{\mathit{x}}=\frac{5}{195}=\frac{1}{39}$
⇒ $\mathit{x}=39$ km/hr