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Problems On Trains
Question 26 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
30 | |
40 | |
45 | |
25 |
Question 26 Explanation:
\begin{align} & {\text{Speed}}\, {\text{of}}\, {\text{the}}\, {\text{train}}\, {\text{relative}}\, {\text{to}}\, {\text{man}} \cr & = \left( {63 - 3} \right)\, {\text{km/hr}} \cr & = 60\, {\text{km/hr}} \cr & = \left( {60 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} \cr & \therefore {\text{Time}}\, {\text{taken}}\, {\text{to}}\, {\text{pass}}\, {\text{the}}\, {\text{man}} \cr & = \left( {500 \times \frac{3}{{50}}} \right)\, \sec \cr & = 30\, \sec \cr\end{align}
Question 27 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Two trains of equal length are running on parallel lines in the same directions at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is?
82 m | |
80 m | |
72 m | |
50 m |
Question 27 Explanation:
\begin{align} & {\text{Let the length of each train be }}x{\text{ metres}} \cr & {\text{Then distance covered}} \cr & {\text{ = 2x metres}} \cr & {\text{Relative speed}} \cr & {\text{ = (46}} - {\text{36)km/hr}} \cr & {\text{ = }}\left( {10 \times \frac{5}{{18}}} \right)m/\sec \cr & = \left( {\frac{{25}}{9}} \right)m/\sec \cr & \therefore \frac{{2x}}{{36}} = \frac{{25}}{9} \Leftrightarrow 2x = 100 \Leftrightarrow x = 50 \cr\end{align}
Question 28 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
120 m | |
240 m | |
300 m | |
None of these |
Question 28 Explanation:
\begin{align} & {\text{Speed}} = \left( {54 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} = 15\, {\text{m/sec}} \cr & {\text{Length}}\, {\text{of}}\, {\text{the}}\, {\text{train}} = \left( {15 \times 20} \right){\text{m}} = 300\, {\text{m}} \cr & {\text{Let}}\, {\text{the}}\, {\text{length}}\, {\text{of}}\, {\text{the}}\, {\text{platform}}\, {\text{be}}\, x\, {\text{metres}} \cr & {\text{Then}}, \, \frac{{x + 300}}{{36}} = 15 \cr & \Rightarrow x + 300 = 540 \cr & \Rightarrow x = 240\, {\text{m}} \cr\end{align}
Question 29 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Two trains of equal lengths takes 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 miters, in what time ( in seconds) will they cross each other traveling in opposite direction?
15 | |
10 | |
20 | |
12 |
Question 29 Explanation:
\begin{align} & {\text{Speed of the train}} \cr & {\text{ = }}\left( {\frac{{120}}{{10}}} \right){\text{ m/sec}} \cr & {\text{ = 12 m/sec}} \cr & {\text{Speed of the second train}} \cr & {\text{ = }}\left( {\frac{{120}}{{15}}} \right){\text{ m/sec}} \cr & {\text{ = 8 m/sec}} \cr & {\text{Relative speed}} \cr & {\text{ = (12 + 8)m/sec}} \cr & {\text{ = 20 m/sec}} \cr & \therefore {\text{Required time}} \cr & {\text{ = }}\frac{{\left( {120 + 120} \right)}}{{20}}\, \sec \cr & = 12\, \sec \cr\end{align}
Question 30 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
240 m | |
270 m | |
230 m | |
260 m |
Question 30 Explanation:
\begin{align} & {\text{Speed}} = \left( {72 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = 20\, {\text{m/sec}} \cr & {\text{Time}} = 26\, {\text{sec}} \cr & {\text{Let}}\, {\text{the}}\, {\text{length}}\, {\text{of}}\, {\text{the}}\, {\text{train}}\, {\text{be}}\, x\, {\text{metres}}{\text{.}} \cr & {\text{Then}}, \, \frac{{x + 250}}{{26}} = 20 \cr & \Rightarrow x + 250 = 520 \cr & \Rightarrow x = 270 \cr\end{align}
There are 30 questions to complete.