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Problems On Trains
Question 56 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Train A passes a lamp post in 9 seconds and 700 meter long platfrom in 30 seconds. How much time will the same train take to cross a platfrom which is 800 meters long? (in seconds)
31 | |
30 | |
32 | |
33 |
Question 56 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}
Question 57 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:
36 | |
49 | |
48 | |
45 |
Question 57 Explanation:
\begin{align} & {\text{Relative}}\, {\text{speed}} = \left( {60 + 90} \right)\, {\text{km/hr}} \cr & = \left( {150 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} \cr & = \left( {\frac{{125}}{3}} \right)\, {\text{m/sec}} \cr & {\text{Distance}}\, {\text{covered}} \cr & = \left( {1.10 + 0.9} \right)\, km \cr & = 2\, km \cr & = \, 2000\, m \cr & {\text{Required}}\, {\text{time}} \cr & = \left( {2000 \times \frac{3}{{125}}} \right)\, {\text{sec}} \cr & = 48\, sec \cr\end{align}
Question 58 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
450 m | |
600 m | |
400 m | |
560 m |
Question 58 Explanation:
\begin{align} & {\text{Let}}\, {\text{the}}\, {\text{length}}\, {\text{of}}\, {\text{the}}\, {\text{first}}\, {\text{train}}\, {\text{be}}\, x\, {\text{metres}} \cr & {\text{Then, }}\, {\text{the}}\, {\text{length}}\, {\text{of}}\, {\text{the}}\, {\text{second}}\, {\text{train}}\, {\text{is}}\, \left( {\frac{x}{2}} \right)\, {\text{metres}} \cr & {\text{Relative}}\, {\text{speed}} = \left( {48 + 42} \right)\, {\text{kmph}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = \left( {90 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = 25\, {\text{m/sec}} \cr & \therefore \frac{{\left[ {x + \left( {x/2} \right)} \right]}}{{25}} = 12 \cr & or\, \frac{{3x}}{2} = 300 \cr & or\, x = 200 \cr & \therefore {\text{Length}}\, {\text{of}}\, {\text{first}}\, {\text{train}} = 200\, {\text{m}} \cr & {\text{Let}}\, {\text{the}}\, {\text{length}}\, {\text{of}}\, {\text{platform}}\, {\text{be}}\, y\, {\text{metres}} \cr & {\text{Speed}}\, {\text{of}}\, {\text{the}}\, {\text{first}}\, {\text{train}} \cr & = \left( {48 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} \cr & = \frac{{40}}{3}\, {\text{m/sec}} \cr & \therefore \left( {200 + y} \right) \times \frac{3}{{40}} = 45 \cr & \Rightarrow 600 + 3y = 1800 \cr & \Rightarrow y = 400\, {\text{m}} \cr\end{align}
Question 59 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train is moving at a speed of 132 km/hr. If the length of the train is 110 meters, how long it will take to cross a railway platform 165 meter long?
5 second | |
10 second | |
15 second | |
7.5 second |
Question 59 Explanation:
\begin{align} & {\text{Speed = 132 km/hr }} \cr & {\text{ = 132}} \times \frac{5}{{18}}{\text{m/sec}} \cr & {\text{ = }}\frac{{110}}{3}m/\sec \cr & T = \frac{D}{S} \cr & \, \, \, \, \, \, = \frac{{110 + 165}}{{\frac{{100}}{3}}} \cr & \, \, \, \, \, \, = \frac{{3\left( {275} \right)}}{{110}} \cr & \, \, \, \, \, \, = 7.5\sec \cr\end{align}
Question 60 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
6 sec | |
7 sec | |
5 sec | |
10 sec |
Question 60 Explanation:
\begin{align} & {\text{Speed}}\, {\text{of}}\, {\text{train}}\, {\text{relative}}\, {\text{to}}\, {\text{man}} \cr & = \left( {60 + 6} \right)\, {\text{km/hr}} \cr & = 66\, {\text{km/hr}} \cr & = \left( {66 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} \cr & = \left( {\frac{{55}}{3}} \right)\, {\text{m/sec}} \cr & \therefore {\text{Time}}\, {\text{taken}}\, {\text{to}}\, {\text{pass}}\, {\text{the}}\, {\text{man}} \cr & = \left( {110 \times \frac{3}{{55}}} \right){\text{sec}} = 6\, {\text{sec}} \cr\end{align}
There are 60 questions to complete.