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Problems On Trains
Question 16 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
54 m | |
72 m | |
45 m | |
50 m |
Question 16 Explanation:
\begin{align} & 2\, kmph = \left( {2 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = \frac{5}{9}\, {\text{m/sec}} \cr & 4\, kmph = \left( {4 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = \frac{{10}}{9}\, {\text{m/sec}} \cr & {\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 & {\text{Then}}, \, \left( {\frac{x}{{y - \frac{5}{9}}}} \right) = 9\, {\text{and}}\, \left( {\frac{x}{{y - \frac{{10}}{9}}}} \right) = 10 \cr & \therefore 9y - 5 = x\, {\text{and}}\, 10\left( {9y - 10} \right) = 9x \cr & \Rightarrow 9y - x = 5\, {\text{and}}\, 90y - 9x = 100 \cr & {\text{On}}\, {\text{solving, }}\, {\text{we}}\, {\text{get}}:\, x = 50 \cr & \therefore {\text{Length}}\, {\text{of}}\, {\text{the}}\, {\text{train}}\, {\text{is}}\, 50\, m \cr\end{align}
Question 17 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
245 m | |
200 m | |
225 m | |
250 m |
Question 17 Explanation:
\begin{align} & {\text{Speed}} = \left( {45 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = \left( {\frac{{25}}{2}} \right)\, {\text{m/sec}} \cr & {\text{Time}} = 30\, {\text{sec}} \cr & {\text{Let}}\, {\text{the}}\, {\text{length}}\, {\text{of}}\, {\text{bridge}}\, {\text{be}}\, x\, {\text{metres}} \cr & {\text{Then}}, \, \frac{{130 + x}}{{30}} = \frac{{25}}{2} \cr & \Rightarrow 2\left( {130 + x} \right) = 750 \cr & \Rightarrow x = 245\, m \cr\end{align}
Question 18 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
50 km/hr | |
54 km/hr | |
55 km/hr | |
45 km/hr |
Question 18 Explanation:
\begin{align} & {\text{Speed}}\, {\text{of}}\, {\text{the}}\, {\text{train}}\, {\text{relative}}\, {\text{to}}\, {\text{man}} \cr & = \left( {\frac{{125}}{{10}}} \right){\text{m/sec}} \cr & = \left( {\frac{{25}}{2}} \right){\text{m/sec}} \cr & = \left( {\frac{{25}}{2} \times \frac{{18}}{5}} \right){\text{km/hr}} \cr & = 45\, {\text{km/hr}} \cr & {\text{Let}}\, {\text{the}}\, {\text{speed}}\, {\text{of}}\, {\text{the}}\, {\text{train}}\, {\text{be}}\, x\, {\text{km/hr}}. \cr & Then, \, relative\, speed = \left( {x - 5} \right)\, {\text{km/hr}} \cr & \therefore x - 5 = 45 \Rightarrow x = 50\, {\text{km/hr}} \cr\end{align}
Question 19 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train of length 500 feet crosses a platform of length 700 feet in 10 seconds. The speed of the train is?
100 ft/second | |
120 ft/second | |
85 ft/second | |
70 ft/second |
Question 19 Explanation:
\begin{align} & {\text{Speed of the train}} \cr & {\text{ = }}\frac{{700 + 500}}{{10}} \cr & {\text{ = 120 ft/second}} \cr\end{align}
Question 20 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train 110 meters 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?
10 sec | |
7 sec | |
6 sec | |
5 sec |
Question 20 Explanation:
\begin{align} & {\text{Speed of train relative to man}} \cr & {\text{ = }}\left( {60 + 6} \right){\text{km/hr}} \cr & = 66\, {\text{km/hr}} \cr & = \left( {66 \times \frac{5}{{18}}} \right)m/\sec \cr & = \left( {\frac{{55}}{3}} \right)m/\sec \cr & \therefore {\text{Time taken to pass the man}} \cr & \left( {100 \times \frac{3}{{55}}} \right)\sec = 6\, \sec \cr\end{align}
There are 20 questions to complete.