SSC CHSL 7 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, ⇒ $\frac{708}{\mathit{y}}-\frac{708}{\mathit{x}}=6$
⇒ $\frac{1}{\mathit{y}}-\frac{1}{\mathit{x}}=\frac{6}{708}=\frac{1}{118}$ ----- (i)
If speed of express train is doubled = 2y km/hr
⇒ $\frac{708}{\mathit{x}}-\frac{708}{2\mathit{y}}=3$
⇒ $\frac{1}{\mathit{x}}-\frac{1}{2\mathit{y}}=\frac{3}{708}=\frac{1}{236}$ ---- (ii)
Adding equations (i) and (ii), we get :
⇒ $\frac{1}{\mathit{y}}-\frac{1}{2\mathit{y}}=\frac{1}{118}+\frac{1}{236}$
⇒ $\frac{1}{2\mathit{y}}=\frac{3}{236}$
⇒ $\mathit{y}=\frac{118}{3}$ km/hr
∴ Speed of Rajdhani = $\frac{1}{\mathit{x}}=\frac{3}{118}-\frac{1}{118}$
⇒ $\frac{1}{\mathit{x}}=\frac{2}{118}=\frac{1}{59}$
⇒ $\mathit{x}=59$ km/hr