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Problems On Trains
Question 61 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train takes 9 sec to cross a pole. If the speed of the train is 48 kmph, then length of the train is?
120 m | |
80 m | |
90 m | |
150 m |
Question 61 Explanation:
\begin{align} & {\text{Time taken by train to cross a pole}} \cr & {\text{ = 9 sec}} \cr & {\text{Distance covered in crossing a pole}} \cr & {\text{ = length of train}} \cr & {\text{Speed of the train}} \cr & {\text{ = 48 km/h}} \cr & = \left( {\frac{{48 \times 5}}{{18}}} \right)m/\sec \cr & = \frac{{40}}{3}m/\sec \cr & \therefore {\text{Length of the train}} \cr & {\text{ = Speed }} \times {\text{Time}} \cr & {\text{ = }}\frac{{40}}{3} \times 9 \cr & {\text{ = 120 m}} \cr\end{align}
Question 62 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
78 km/hr | |
81 km/hr | |
66 km/hr | |
72 km/hr |
Question 62 Explanation:
\begin{align} & 4.5\, {\text{km/hr}} = \left( {4.5 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = \frac{5}{4}\, {\text{m/sec}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = 1.25\, {\text{m/sec, }}\, {\text{and}} \cr & 5.4\, km/hr = \left( {5.4 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = \frac{3}{2}\, {\text{m/sec}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = 1.5\, {\text{m/sec}} \cr & {\text{Let}}\, {\text{the}}\, {\text{speed}}\, {\text{of}}\, {\text{the}}\, {\text{train}}\, {\text{be}}\, x\, {\text{m/sec}} \cr & {\text{Then}}, \, \left( {x - 1.25} \right) \times 8.4 = \left( {x - 1.5} \right) \times 8.5 \cr & \Rightarrow 8.4x - 10.5 = 8.5x - 12.75 \cr & \Rightarrow 0.1x = 2.25 \cr & \Rightarrow x = 22.5 \cr & \therefore {\text{Speed}}\, {\text{of}}\, {\text{the}}\, {\text{train}} \cr & = \left( {22.5 \times \frac{{18}}{5}} \right)\, {\text{km/hr}} \cr & = 81\, {\text{km/hr}} \cr\end{align}
Question 63 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Two trains of lenths 120 m and 90 m are running with speed of 80 km/hr and 55 km/hr respectively towards each other on parallel lines. If they are 90 m apart, after how many seconds they will cross each other?
8 sec | |
9 sec | |
5.6 sec | |
7.2 sec |
Question 63 Explanation:
\begin{align} & {\text{Relative speed}} \cr & {\text{ = (80 + 55)km/hr}} \cr & {\text{ = 135 km/hr}} \cr & {\text{ = }}\left( {135 \times \frac{5}{{18}}} \right)m/\sec \cr & = \left( {\frac{{75}}{2}} \right)m/\sec \cr & {\text{Distance covered}} \cr & {\text{ = (120 + 90 + 90)m}} \cr & {\text{ = 300m}} \cr & {\text{Required time}} \cr & {\text{ = }}\left( {300 \times \frac{2}{{75}}} \right)\sec \cr & = 8\sec \cr\end{align}
Question 64 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Two trains A and B start running together from the same point in the same direction, at the speed of 60 kmph and 72 kmph respectively. If the length of each of the trains is 240 meters, how long will it take for B to cross train A?
1 min 24 sec | |
1 min 12 sec | |
2 min 12 sec | |
2 min 24 sec |
Question 64 Explanation:
\begin{align} & {\text{Relative speed}} \cr & {\text{ = (72}} - {\text{60) km/hr}} \cr & {\text{ = 12 km/hr}} \cr & = \left( {12 \times \frac{5}{{18}}} \right)m/\sec \cr & = \left( {\frac{{10}}{3}} \right)m/\sec \cr & {\text{Total distance covered}} \cr & {\text{ = Sum of lengths of trains}} \cr & {\text{ = (240 + 240) m}} \cr & {\text{ = 480 m}} \cr & {\text{Time taken}} \cr & {\text{ = }}\left( {480 \times \frac{3}{{10}}} \right)\sec \cr & = 144\sec \cr & = 2\min \, 24sec \cr\end{align}
Question 65 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Two trains start at the same time from A and B and proceed toward each other at the sped of 75 km/hr and 50 km/hr respectively. When both meet at a point in between, one train was found to have traveled 175 km more then the other. Find the distance between A and B?
758 km | |
785 km | |
875 km | |
857 km |
Question 65 Explanation:
\begin{align} & {\text{Let the trains meet after 1 hours}} \cr & {\text{Speed of train A}} \cr & {\text{ = 75 km/hr}} \cr & {\text{Speed of train B}} \cr & {\text{ = 50 km/hr}} \cr & {\text{Distance covered by train A}} \cr & {\text{ = 75}} \times {\text{t = 75t}} \cr & {\text{Distance covered by train B}} \cr & {\text{ = 50}} \times {\text{t = 50t}} \cr & {\text{Distance}}\, {\text{ = Speed }} \times {\text{Time}} \cr & {\text{According to question}} \cr & 75{\text{t}} - 50{\text{t}} = 175 \cr & \Rightarrow 25{\text{t}} = 175 \cr & \Rightarrow {\text{t}} = \frac{{175}}{{25}} = 7\, {\text{hour}} \cr & \therefore {\text{Distance between A and B }} \cr & {\text{ = 75t}} + 50{\text{t}} = 125{\text{t}} \cr & = 125 \times 7 = 875\, {\text{km}} \cr\end{align}
There are 65 questions to complete.