YOU CAN DOWNLOAD 200+ SUBJECTS PDF BOOK FOR COMPETITIVE EXAMINATIONS
Problems On Trains
Question 51 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:
30 km/hr | |
75 km/hr | |
60 km/hr | |
45 km/hr |
Question 51 Explanation:
\begin{align} & {\text{Let}}\, {\text{the}}\, {\text{speed}}\, {\text{of}}\, {\text{the}}\, {\text{slower}}\, {\text{train}}\, {\text{be}}\, x\, {\text{m/sec}} \cr & {\text{Then, }}\, {\text{speed}}\, {\text{of}}\, {\text{the}}\, {\text{faster}}\, {\text{train}} = 2x\, {\text{m/sec}} \cr & {\text{Relative}}\, {\text{speed}} = \, \left( {x + 2x} \right)\, {\text{m/sec}} = 3x\, {\text{m/sec}} \cr & \therefore \frac{{\left( {100 + 100} \right)}}{8} = 3x \cr & \Rightarrow 24x = 200 \cr & \Rightarrow x = \frac{{25}}{3} \cr & {\text{So, }}\, {\text{speed}}\, {\text{of}}\, {\text{the}}\, {\text{faster}}\, {\text{train}}\, = \frac{{50}}{3}\, {\text{m/sec}} \cr & = \left( {\frac{{50}}{3} \times \frac{{18}}{5}} \right)\, {\text{km/hr}} \cr & = 60\, {\text{km/hr}} \cr\end{align}
Question 52 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train B speeding with 120 kmph crosses another train C running in the same direction, in 2 minutes. If the lengths of the trains B and C be 100m and 200m respectively, what is the speed (in kmph) of the train C?
129 km | |
123 km | |
127 km | |
111 km |
Question 52 Explanation:
\begin{align} & {\text{Relative speed of the trains }} \cr & {\text{ = }}\left( {\frac{{100 + 200}}{{2 \times 60}}} \right){\text{m/sec}} \cr & {\text{ = }}\left( {\frac{5}{2}} \right){\text{m/sec}} \cr & {\text{Speed of train B}} \cr & {\text{ = 120 kmph}} \cr & = \left( {120 \times \frac{5}{{18}}} \right){\text{m/sec}} \cr & {\text{ = }}\left( {\frac{{100}}{3}} \right){\text{m/sec}} \cr & {\text{Let the speed of second train be }}x{\text{ m/sec}} \cr & {\text{Then, }}x - \frac{{100}}{3} = \frac{5}{2} \cr & \Rightarrow x = \left( {\frac{5}{2} + \frac{{100}}{3}} \right) \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, = \left( {\frac{{215}}{6}} \right){\text{m/sec}} \cr & \therefore {\text{Speed of second train}} \cr & {\text{ = }}\left( {\frac{{215}}{6} \times \frac{{18}}{5}} \right){\text{ kmph}} \cr & {\text{ = 129 kmph}} \cr\end{align}
Question 53 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
20 | |
12 | |
10 | |
15 |
Question 53 Explanation:
\begin{align} & {\text{Speed}}\, {\text{of}}\, {\text{the}}\, {\text{first}}\, {\text{train}} \cr & = \left( {\frac{{120}}{{10}}} \right)\, {\text{m/sec}} \cr & = 12\, {\text{m/sec}} \cr & {\text{Speed}}\, {\text{of}}\, {\text{the}}\, {\text{second}}\, {\text{train}} \cr & \left( {\frac{{120}}{{15}}} \right)\, {\text{m/sec}} \cr & = 8\, {\text{m/sec}} \cr & {\text{Relative}}\, {\text{speed}} = \left( {12 + 8} \right) = 20\, {\text{m/sec}} \cr & \therefore {\text{Required}}\, {\text{time}} \cr & = \left[ {\frac{{\left( {120 + 120} \right)}}{{20}}} \right]\, {\text{sec}} \cr & = 12\, {\text{sec}} \cr\end{align}
Question 54 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train running at the speed of 84 km/hr passes a man walking in opposite direction at the speed of 6 km/hr in 4 seconds. What is the length of train (in meter)?
120 | |
150 | |
90 | |
100 |
Question 54 Explanation:
\begin{align} & {\text{Let length of train }} \cr & {\text{ = }}l\, {\text{metre}} \cr & \Rightarrow {\text{Time }} \cr & {\text{ = }}\frac{{{\text{total distance}}}}{{{\text{relative speed in opposite direction}}}} \cr & \Rightarrow 4\sec \, = \, \frac{{l + 0}}{{\left( {84 + 6} \right) \times \frac{5}{{18}}{\text{m/s}}}} \cr & \Rightarrow 4\, = \frac{l}{{90 \times \frac{5}{{18}}}} \cr & \Rightarrow \, l\, = \, 100\, {\text{m}} \cr & \therefore {\text{ length of the train = 100 m}} \cr\end{align}
Question 55 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Train A passes a lamp post in 9 seconds and 700 meter long platform in 30 seconds. How much time will the same train take to cross a platform which is 800 meters long? (in seconds)
31 | |
33 | |
32 | |
30 |
Question 55 Explanation:
\begin{align} & {\text{Let the length of train be x m}} \cr & {\text{When a train crosses a light }} \cr & {\text{post in 9 second the distance covered}} \cr & {\text{ = length of train }} \cr & \Rightarrow {\text{speed of train = }}\frac{x}{9} \cr & {\text{Distance covered in crossing a}} \cr & {\text{700 meter platfrom in 30 seconds}} \cr & {\text{ = Length of platfrom + length of train}} \cr & {\text{Speed of train = }}\frac{{x + 700}}{9} \cr & \Rightarrow \frac{x}{9} = \frac{{x + 700}}{{30}}\left[ {\because {\text{Speed = }}\frac{{{\text{Distance}}}}{{{\text{Time}}}}} \right] \cr & \Rightarrow \frac{x}{3} = \frac{{x + 700}}{{10}} \cr & \Rightarrow 10x = 3x + 2100 \cr & \Rightarrow 10x - 3x = 2100 \cr & \Rightarrow 7x = 2100 \cr & \Rightarrow x = \frac{{2100}}{7} = 300{\text{m}} \cr & {\text{When the length of the platform be 800m, }} \cr & {\text{then time T be taken by train to cross 800m}} \cr & {\text{long platfrom}} \cr & \frac{x}{9} = \frac{{x + 800}}{T} \cr & \Rightarrow Tx = 9x + 7200 \cr & \Rightarrow 300T = 2700 + 7200 \cr & \Rightarrow 300T = 9900 \cr & \Rightarrow T = \frac{{9900}}{{300}} = 33{\text{ seconds}} \cr\end{align}
There are 55 questions to complete.