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Problems On Trains
Question 11 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train 132 m long passes a telegraph pole in 6 seconds. Find the speed of the train?
80 km/hr | |
72 km/hr | |
79.2 km/hr | |
70 km/hr |
Question 11 Explanation:
\begin{align} & {\text{Speed}} \cr & {\text{ = }}\left( {\frac{{132}}{6}} \right){\text{m/sec}} \cr & {\text{ = }}\left( {22 \times \frac{{18}}{5}} \right){\text{km/sec}} \cr & {\text{ = 79}}{\text{.2 km/hr}} \cr\end{align}
Question 12 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
150 m | |
200 m | |
50 m | |
Data inadequate |
Question 12 Explanation:
\begin{align} & {\text{Let}}\, {\text{the}}\, {\text{length}}\, {\text{of}}\, {\text{the}}\, {\text{train}}\, {\text{be}}\, x\, {\text{metres}} \cr & \, {\text{and}}\, {\text{its}}\, {\text{speed}}\, {\text{by}}\, y\, {\text{m/sec}} \cr & Then, \, \frac{x}{y} = 15\, \, \, \, \, \, \Rightarrow \, \, \, \, \, y = \frac{x}{{15}} \cr & \therefore \frac{{x + 100}}{{25}} = \frac{x}{{15}} \cr & \Rightarrow 15\left( {x + 100} \right) = 25x \cr & \Rightarrow 15x + 1500 = 25x \cr & \Rightarrow 1500 = 10x \cr & \Rightarrow x = 150m \cr\end{align}
Question 13 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
3.6 sec | |
36 sec | |
72 sec | |
18 sec |
Question 13 Explanation:
\begin{align} & {\text{Speed}}\, {\text{of}}\, {\text{train}}\, {\text{relative}}\, {\text{to}}\, {\text{jogger}} \cr & = \left( {45 - 9} \right)\, {\text{km/hr}} \cr & = 36\, {\text{km/hr}} \cr & \left( {36 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} \cr & = 10\, {\text{m/sec}} \cr & {\text{Distance}}\, {\text{to}}\, {\text{be}}\, {\text{covered}} \cr & = \left( {240 + 120} \right)\, m \cr & = 360\, m \cr & \therefore {\text{Time}}\, {\text{taken}} \cr & = \left( {\frac{{360}}{{10}}} \right)\, {\text{sec}} \cr & = 36\, {\text{sec}} \cr\end{align}
Question 14 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train cover a distance of 3584 km in 2 days 8 hours. If it covers 1440 km on the first day and 1608 km on the second day, by how much does the average speed of the train for the remaining part of the journey differ from that for the entire journey?
2 km/h | |
3 km/h | |
4 km/h | |
10 km/h |
Question 14 Explanation:
\begin{align} & {\text{Given, }} \cr & {\text{Train cover 3584 kms in 2 days 8 hours}} \cr & \left( {2\, {\text{days 8 hours = }}\frac{7}{3}{\text{ days}}} \right) \cr & {\text{Average speed = }}\frac{{3584}}{7} \cr & {\text{ = 1536 km/day = }}\frac{{1536}}{{24}}{\text{ = 64 km/h}} \cr & {\text{Distance covered in two days}} \cr & {\text{ = 1440 + 1608 = 3048 km}} \cr & {\text{Remaining distance for third day}} \cr & {\text{ = 3584 }} - {\text{3048 = 536 km}} \cr & {\text{Third day 536 km is covered in }} \cr & {\text{8 hour with speed of}} \cr & {\text{ = }}\frac{{536}}{8} = 67{\text{ km/h }} \cr & {\text{( 3rd day total 536 km distance}} \cr & {\text{ covered by 67 km/hr in 8 hr)}} \cr & \therefore {\text{Difference of average speedm}} \cr & {\text{ = 67}} - {\text{64 = 3 km/hr}} \cr\end{align}
Question 15 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train travelling at a speed of 75 mph enters a tunnel 3 1/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
2.5 min | |
3.2 min | |
3 min | |
3.5 min |
Question 15 Explanation:
\begin{align} & {\text{Total}}\, {\text{distance}}\, {\text{covered}} \cr & = \left( {\frac{7}{2} + \frac{1}{4}} \right)\, {\text{miles}} \cr & = \frac{{15}}{4}\, {\text{miles}} \cr & \therefore {\text{Time}}\, {\text{taken}} \cr & = \left( {\frac{{15}}{{4 \times 75}}} \right)\, {\text{hrs}} \cr & = \frac{1}{{20}}\, {\text{hrs}} \cr & = \left( {\frac{1}{{20}} \times 60} \right)\, \min \cr & = 3\, \min \cr\end{align}
There are 15 questions to complete.