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Problems On Trains
Question 6 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
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:
2 : 3 | |
6 : 7 | |
9 : 16 | |
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 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
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?
75 kmph | |
86.4 kmph | |
63 kmph | |
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 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
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:
54 km/hr | |
48 km/hr | |
82 km/hr | |
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 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
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?
1 hr | |
3 hr | |
21/2 hr | |
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 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
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:
500 | |
130 | |
360 | |
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.