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Problems On Trains
Question 36 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
1 : 3 | |
3 : 2 | |
3 : 4 | |
None of these |
Question 36 Explanation:
\begin{align} & {\text{Let}}\, {\text{the}}\, {\text{speeds}}\, {\text{of}}\, {\text{the}}\, {\text{two}}\, {\text{trains}}\, {\text{be}}\, x\, {\text{m/sec}} \cr & {\text{and}}\, y\, {\text{m/sec}}\, {\text{respectively}}. \cr & {\text{Then, }}\, {\text{length}}\, {\text{of}}\, {\text{the}}\, {\text{first}}\, {\text{train}} = 27x\, {\text{metres}}, \cr & {\text{and}}\, {\text{length}}\, {\text{of}}\, {\text{the}}\, {\text{second}}\, {\text{train}} = 17y\, {\text{metres}}. \cr & \therefore \frac{{27x + 17y}}{{x + y}} = 23 \cr & \Rightarrow 27x + 17y = 23x + 23y \cr & \Rightarrow 4x = 6y \cr & \Rightarrow \frac{x}{y} = \frac{3}{2} \cr\end{align}
Question 37 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train which is moving at an average speed of 40 km/h reaches its destination on time. When its average speed reduces to 35 km/h, then it reaches its destination 15 minutes late. The distance traveled by the train is?
70 km | |
40 km | |
30 km | |
80 km |
Question 37 Explanation:
\begin{align} & {\text{Average speed of train}} \cr & {\text{ = 40 km/hr}} \cr & {\text{Reach at its destination at on time }} \cr & {\text{New average speed of train}} \cr & {\text{ = 35 km/h}} \cr & {\text{Time = 15 minutes}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, {\text{ = }}\frac{{15}}{{60}}{\text{hours }} \cr & {\text{Then distance travelled}} \cr & {\text{ = }}\frac{{40 \times 35}}{{40 - 35}}{\text{ }} \times \frac{{15}}{{60}} \cr & {\text{ = }}\frac{{40 \times 35}}{5}{\text{ }} \times \frac{{15}}{{60}} \cr & {\text{ = 70}}\, {\text{km}} \cr\end{align}
Question 38 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
The Ghaziabad - Hapur - Meerut EMU and the Meerut - Hapur - Ghaziabad EMU start at the same time from Ghaziabad and Meerut and proceed towards each other at 16 km/hr and 21 km/hr respectively. When they meet, it is found that one train has traveled 60 km more than the other . The distance between two stations is?
440 km | |
444 km | |
445 km | |
450 km |
Question 38 Explanation:
\begin{align} & {\text{At the time of meeting, }} \cr & {\text{let the distance travelled by the}} \cr & {\text{first train be }}x{\text{ km}}{\text{.}} \cr & {\text{Then distance travelled by the }} \cr & {\text{second train is (}}x{\text{ + 60) km}} \cr & \therefore \frac{x}{{16}} = \frac{{x + 16}}{{21}} \cr & \Rightarrow 21x = 16x + 960 \cr & \Rightarrow 5x = 960 \Rightarrow x = 192 \cr & {\text{Hence, }} \cr & {\text{distance between two stations}} \cr & {\text{ = (192 + 192 + 60) km}} \cr & {\text{ = 444 km}}{\text{.}} \cr\end{align}
Question 39 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
100 sec | |
150 sec | |
65 sec | |
89 sec |
Question 39 Explanation:
\begin{align} & {\text{Speed}} = \left( {\frac{{240}}{{24}}} \right)\, {\text{m/sec}} = 10\, {\text{m/sec}} \cr & \therefore {\text{Required}}\, {\text{time}} \cr & {\text{ = }}\, \left( {\frac{{240 + 650}}{{10}}} \right)\, {\text{sec}}. \cr & = 89\, sec. \cr\end{align}
Question 40 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
240 m | |
320 m | |
230 m | |
260 m |
Question 40 Explanation:
\begin{align} & {\text{Relative}}\, {\text{speed}} \cr & = \left( {120 + 80} \right)\, {\text{km/hr}} \cr & = \left( {200 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} \cr & = \left( {\frac{{500}}{9}} \right)\, {\text{m/sec}} \cr & {\text{Let}}\, {\text{the}}\, {\text{length}}\, {\text{of}}\, {\text{the}}\, {\text{other}}\, {\text{train}}\, {\text{be}}\, {\text{x}}\, {\text{metres}}{\text{.}} \cr & {\text{Then, }}\, \frac{{x + 270}}{9} = \frac{{500}}{9} \cr & \Rightarrow x + 270 = 500 \cr & \Rightarrow x = 230 \cr\end{align}
There are 40 questions to complete.