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Problems On Trains
Question 41 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
79.2 km/hr | |
79 km/hr | |
70 km/hr | |
69.5 km/hr |
Question 41 Explanation:
\begin{align} & {\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}}, \, \frac{x}{y} = 8\, \, \, \, \, \, \Rightarrow \, \, \, \, \, x = 8y \cr & {\text{Now}}, \, \frac{{x + 264}}{{20}} = y \cr & \Rightarrow 8y + 264 = 20y \cr & \Rightarrow y = 22 \cr & \therefore {\text{Speed}} = 22\, {\text{m/sec}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = \left( {22 \times \frac{{18}}{5}} \right)\, {\text{km/hr}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = 79.2\, {\text{km/hr}} \cr\end{align}
Question 42 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
What is the speed of a train if it overtakes two persons who are walking in the same direction at the rate of a m/s and (a + 1) m/s and passes them completely in b seconds and (b + 1) seconds respectively?
(a + b) m/s | |
(2a + 1)/2 m/s | |
(2a + 1) m/s | |
(a + b + 1) m/s |
Question 42 Explanation:
\begin{align} & {\text{Let the length of the train be }}x{\text{ metres}} \cr & {\text{and its speed be }}y{\text{ m/s}} \cr & {\text{Then, }} \cr & {\text{ }}\frac{x}{{y - a}}{\text{ = b}}\, \, {\text{and}}\, \cr & \, \frac{x}{{y - \left( {a + 1} \right)}} = \left( {b + 1} \right) \cr & \Leftrightarrow {\text{ }}x{\text{ = }}b\left( {y - a} \right){\text{ and}} \cr & \, \, \, \, \, \, \, \, \, \, {\text{ }}x = \left( {b + 1} \right)\left( {y - a - 1} \right) \cr & \Leftrightarrow b\left( {y - a} \right) = \left( {b + 1} \right)\left( {y - a - 1} \right) \cr & \Leftrightarrow by - ba = by - ba - b + y - a - 1 \cr & \Leftrightarrow y = \left( {a + b + 1} \right) \cr\end{align}
Question 43 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
24 sec | |
48 sec | |
60 sec | |
12 sec |
Question 43 Explanation:
\begin{align} & {\text{Relative}}\, {\text{speed}} \cr & = \left( {45 + 30} \right)\, {\text{km/hr}} \cr & = \left( {\frac{{125}}{6}} \right)\, {\text{m/sec}} \cr & {\text{We}}\, {\text{have}}\, {\text{to}}\, {\text{find}}\, {\text{the}}\, {\text{time}}\, {\text{taken}}\, {\text{by}}\, {\text{the}} \cr & {\text{slower}}\, {\text{train}}\, {\text{to}}\, {\text{pass}}\, {\text{the}}\, {\text{DRIVER}}\, {\text{of}}\, \cr & {\text{The}}\, {\text{faster}}\, {\text{train}}\, {\text{and}}\, {\text{not}}\, {\text{the}}\, {\text{complete}}\, {\text{train}}{\text{.}} \cr & \cr & {\text{So, }}\, {\text{distance}}\, {\text{covered = Length}}\, {\text{of}}\, {\text{the}}\, {\text{slower}}\, {\text{train}}. \cr & {\text{Therefore, }}\, {\text{Distance}}\, {\text{covered = 500}}\, {\text{m}}. \cr & \therefore {\text{Required}}\, {\text{time}} \cr & = \left( {500 \times \frac{6}{{125}}} \right) \cr & = 24\, \sec \cr\end{align}
Question 44 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
120 metres | |
180 metres | |
150 metres | |
324 metres |
Question 44 Explanation:
\begin{align} & {\text{Speed}} = \left( {60 \times \frac{5}{{18}}} \right){\text{m/sec}} = \left( {\frac{{50}}{3}} \right){\text{m/sec}} \cr & {\text{Length}}\, {\text{of}}\, {\text{the}}\, {\text{train}} = \left( {{\text{Speed}} \times {\text{Time}}} \right) \cr & \therefore {\text{Length}}\, {\text{of}}\, {\text{the}}\, {\text{train}} \cr & = \left( {\frac{{50}}{3} \times 9} \right)m = 150m \cr\end{align}
Question 45 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Two trains 180 meters and 120 meters in length are running towards each other on parallel tracks, one at the rate 65 km/hr and another at 55 km/hr. In how many seconds will they be cross each other from the moment they meet?
9 | |
6 | |
12 | |
15 |
Question 45 Explanation:
\begin{align} & {\text{Time taken by trains to cross each }} \cr & {\text{other in opposite direction}} \cr & {\text{ = }}\frac{{{l...1} + {l...2}}}{{{\text{relative speed in opposite direction}}}} \cr & {\text{ = }}\frac{{\left( {180 + 120} \right)}}{{\left( {65 + 55} \right)}} \cr & {\text{ = }}\frac{{300}}{{120 \times \frac{5}{{18}}}} \cr & {\text{ = 9 seconds}} \cr\end{align}
There are 45 questions to complete.