Subject: General Aptitude · Chapter: Time and Distance · Exam: · Marks: · Difficulty:
Train A travelling at 60 km/hr leaves Mumbai for Delhi at 6 p.m. Train B travelling at 90 km/hr also leaves Mumbai for Delhi at 9 p.m. Train C leaves Delhi for Mumbai at 9 p.m. If all the three trains meet at the same time between Mumbai and Delhi, then what is the speed of train C if the distance between Delhi and Mumbai is 1260 km?
(a)60 km/hr
(b)90 km/hr
(c)120 km/hr
(d)135 km/hr
Answer
Answer (as printed): C
Explanation
Suppose the three trains meet $x$ hours after 9 p.m. Let the speed of train $C$ be $y \mathrm{km} / \mathrm{hr}$. Distance travelled by Train $A$ in ( $x+3$ ) hrs = Distance travelled by Train $B$ in $x$ hrs $$\Rightarrow 60(x+3)=90 x \Rightarrow 30 x=180 \Rightarrow x=6 .$$ Also, dist. travelled by Train $B$ in $x$ hrs + Dist. travelled by train $C$ in $x \mathrm{hrs}=1260 \mathrm{km}$ $$\begin{aligned} & \Rightarrow 90 x+y x=1260 \Rightarrow 540+6 y=1260 \Rightarrow 6 y=720 \Rightarrow y \\ & =120 . \end{aligned}$$ Hence, speed of Train $C=120 \mathrm{km} / \mathrm{hr}$.