# Problems on Train

## Problems On Trains

 Question 1
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
 A 9 B 10 C 10.8 D 9.6
Question 1 Explanation:
\begin{align} & {\text{Relative}}\,{\text{speed}} = \left( {60 + 40} \right)\,{\text{km/hr}} \cr & = \left( {100 \times \frac{5}{{18}}} \right)\,{\text{m/sec}} \cr & = \left( {\frac{{250}}{9}} \right)\,{\text{m/sec}}. \cr & {\text{Distance}}\,{\text{covered}}\,{\text{in}}\,{\text{crossing}}\,{\text{each}}\,{\text{other}} \cr & = \left( {140 + 160} \right)m = 300\,m \cr & {\text{Required}}\,{\text{time}} \cr & = \left( {300 \times \frac{9}{{250}}} \right)\,{\text{sec}} \cr & = \frac{{54}}{5}\,{\text{sec}} \cr & = 10.8\,{\text{sec}} \cr\end{align}

 Question 2
A 100 m long train is going at a speed of 60 km/hr. It will cross a 140 m long railway bridge in-
 A 7.2 sec B 14.4 sec C 3.6 sec D 21.6 sec
Question 2 Explanation:
\begin{align} & {\text{Speed }} \cr & {\text{ = }}\left( {60 \times \frac{5}{{18}}} \right){\text{m/sec}} \cr & {\text{ = }}\frac{{50}}{3}{\text{ m/sec}} \cr & {\text{Total distance covered}} \cr & {\text{ = (100 + 140) m = 240 m}} \cr & \therefore {\text{Required time}} \cr & {\text{ = }}\left( {240 \times \frac{3}{{50}}} \right){\text{sec}} \cr & {\text{ = }}\frac{{72}}{5}{\text{sec}} \cr & {\text{ = 14}}{\text{.4 sec}} \cr\end{align}
 Question 3
Two trains ,A ans B start from stations X and Y towards each other, they take 4 hours 48 minutes and 3 hours 20 minutes to reach Y and X respectively after they meet. If train A is moving at 45 km/hr, then the speed of the train B is?
 A 54 km/hr B 60 km/hr C 37.5 km/hr D 64.80 km/hr
Question 3 Explanation:
\begin{align} & {\text{In these type of questions use the given}} \cr & {\text{below formula to save your valuable time}} \cr & \frac{{{{\text{S}}...1}}}{{{{\text{S}}...2}}}{\text{ = }}\sqrt {\frac{{{{\text{T}}...2}}}{{{{\text{T}}...1}}}} {\text{ }} \cr & {\text{Where }}{{\text{S}}...1}{\text{,}}{{\text{S}}...2}{\text{ and }}{{\text{T}}...1}{\text{, }}{{\text{T}}...2}{\text{ are the respective}} \cr & {\text{speeds and times of the objects}} \cr & \Rightarrow \frac{{45}}{{{{\text{S}}...2}}} = \sqrt {3\frac{1}{3} \div 4\frac{4}{5}} \cr & {\text{ = }}{{\text{S}}...2}{\text{ = 45}} \times \frac{6}{5}{\text{ = 54 km/hr}} \cr & \therefore {\text{Required speed = 54 km/hr}} \cr\end{align}

 Question 4
A train 100 meter long meets a man going in opposite direction at 5 km/h and passes him in 71/5 seconds. What is the speed of the train (in km/hr)?
 A 60 km/h B 45 km/h C 50 km/hr D 55 km/hr
Question 4 Explanation:
\begin{align} & {\text{Relative speed of man \& train}} \cr & {\text{ = }}\frac{{100 \times 5}}{{36}} \times \frac{{18}}{5} \cr & {\text{ = 50km/hr}} \cr & \therefore {\text{speed of train}} \cr & {\text{ = 50}} - {\text{5}} \cr & {\text{ = 45 km/hr}} \cr\end{align}
 Question 5
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
 A 10 a.m. B 10.30 a.m. C 9 a.m. D 11 a.m.
Question 5 Explanation:
\begin{align} & {\text{Suppose}}\,{\text{they}}\,{\text{meet}}\,x\,{\text{hours}}\,{\text{after}}\,{\text{7}}\,{\text{a}}{\text{.m}}. \cr & {\text{Distance}}\,{\text{covered}}\,{\text{by}}\,{\text{A}}\, \cr & {\text{in}}\,x\,{\text{hours = 20x}}\,{\text{km}}{\text{.}} \cr & {\text{Distance}}\,{\text{covered}}\,{\text{by}}\,{\text{B}} \cr & \,{\text{in}}\,\left( {x - 1} \right)\,{\text{hours}} = 25\left( {x - 1} \right)\,km \cr & \therefore 20x + 25\left( {x - 1} \right) = 110 \cr & \Rightarrow 45x = 135 \cr & \Rightarrow x = 3 \cr & {\text{So,}}\,{\text{they}}\,{\text{meet}}\,{\text{at}}\,{\text{10}}\,{\text{a}}{\text{.m}}{\text{.}}\, \cr\end{align}

 Question 6
Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
 A 2 : 3 B 6 : 7 C 9 : 16 D 4 : 3
Question 6 Explanation:
\begin{align} & {\text{Let}}\,{\text{us}}\,{\text{name}}\,{\text{the}}\,{\text{trains}}\,{\text{as}}\,{\text{A}}\,{\text{and}}\,{\text{B}}{\text{.}}\,{\text{Then}}, \cr & \left( {{\text{A's}}\,{\text{speed}}} \right):\left( {{\text{B's}}\,{\text{speed}}} \right) \cr & = \sqrt b :\sqrt a \cr & = \sqrt {16} :\sqrt 9 \cr & = 4:3\, \cr\end{align}
 Question 7
A train, 240 m long, crosses a man walking alone the line in opposite direction at the rate of 3 kmph in 10 seconds. The speed of the train is?
 A 75 kmph B 86.4 kmph C 63 kmph D 83.4 kmph
Question 7 Explanation:
\begin{align} & {\text{Speed of the train relative to man}} \cr & {\text{ = }}\left( {\frac{{240}}{{10}}} \right){\text{m/sec}} \cr & {\text{ = 24 m/sec}} \cr & {\text{ = }}\left( {24 \times \frac{{18}}{5}} \right){\text{ km/sec}} \cr & {\text{ = }}\frac{{432}}{5}{\text{km/hr}} \cr & {\text{Let the speed of the train be x kmph}}{\text{.}} \cr & {\text{Then relative speed = }}\left( {x + 3} \right){\text{kmph}} \cr & \therefore x{\text{ + 3 = }}\frac{{432}}{5} \cr & \Rightarrow x = \frac{{432}}{5} - 3 \cr & \Rightarrow x = \frac{{417}}{5} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 83.4\,{\text{kmph}} \cr\end{align}

 Question 8
A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:
 A 54 km/hr B 48 km/hr C 82 km/hr D 66 km/hr
Question 8 Explanation:
\begin{align} & {\text{Let}}\,{\text{the}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{second}}\,{\text{train}}\,{\text{be}}\,x\,{\text{km/hr}}. \cr & {\text{Relative}}\,{\text{speed}}\, \cr & = \,\left( {x + 50} \right)\,{\text{km/hr}} \cr & = \left[ {\left( {x + 50} \right) \times \frac{5}{{18}}} \right]\,{\text{m/sec}} \cr & = \left[ {\frac{{250 + 5x}}{{18}}} \right]\,{\text{m/sec}} \cr & {\text{Distance}}\,{\text{covered}} \cr & = \left( {108 + 112} \right) = 220\,m \cr & \therefore \frac{{220}}{{\left( {\frac{{250 + 5x}}{{18}}} \right)}} = 6 \cr & \Rightarrow 250 + 5x = 660 \cr & \Rightarrow x = 82\,{\text{km/hr}} \cr\end{align}
 Question 9
Two trains start at the same time for two station A and B toward B and A respectively. If the distance between A and B is 220 km and their speeds are 50 km/hr and 60 km/hr respectively then after how much time will they meet each other?
 A 1 hr B 3 hr C 21/2 hr D 2 hr
Question 9 Explanation:
\begin{align} & {\text{Relative speed}} \cr & {\text{ = 60 + 50}} \cr & {\text{ = 110 km/h}} \cr & {\text{Time taken}} \cr & {\text{ = }}\frac{{220}}{{110}} \cr & {\text{ = 2 hr}} \cr\end{align}

 Question 10
A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:
 A 500 B 130 C 360 D 540
Question 10 Explanation:
\begin{align} & {\text{Speed}} = \left( {78 \times \frac{5}{{18}}} \right)\,{\text{m/sec}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{65}}{3}} \right)\,{\text{m/sec}} \cr & {\text{Time = }}\,{\text{1}}\,{\text{minute = 60}}\,{\text{second}}. \cr & {\text{Let}}\,{\text{the}}\,{\text{length}}\,{\text{of}}\,{\text{the}}\,{\text{tunnel}}\,{\text{be}}\,x\,{\text{metres}}. \cr & {\text{Then}},\,\left( {\frac{{800 + x}}{{60}}} \right) = \frac{{65}}{3} \cr & \Rightarrow 3\left( {800 + x} \right) = 3900 \cr & \Rightarrow x = 500 \cr\end{align}
There are 10 questions to complete.