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Problems On Trains
Question 31 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Two trains of equal length are running on parallel lines in the same direction 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 | |
72 m | |
50 m | |
80 m |
Question 31 Explanation:
\begin{align} & {\text{Let}}\, {\text{the}}\, {\text{length}}\, {\text{of}}\, {\text{each}}\, {\text{train}}\, {\text{be}}\, x\, {\text{metres}}. \cr & {\text{Then, }}\, {\text{distance}}\, {\text{covered}} = 2x\, {\text{metres}}. \cr & {\text{Relative}}\, {\text{speed}} \cr & = \left( {46 - 36} \right)\, {\text{km/hr}} \cr & = \left( {10 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} \cr & = \left( {\frac{{25}}{9}} \right)\, {\text{m/sec}} \cr & \therefore \frac{{2x}}{{36}} = \frac{{25}}{9} \cr & \Rightarrow 2x = 100 \cr & \Rightarrow x = 50 \cr\end{align}
Question 32 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
40 sec | |
42 sec | |
48 sec | |
45 sec |
Question 32 Explanation:
\begin{align} & {\text{Formula}}\, {\text{for}}\, {\text{converting}}\, {\text{from}}\, {\text{km/hr}}\, {\text{to}}\, {\text{m/s:}} \cr & X\, {\text{km/hr}} = \left( {X \times \frac{5}{{18}}} \right)\, {\text{m/s}} \cr & {\text{Therefore, }}\, {\text{Speed}} \cr & = \left( {45 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} = \frac{{25}}{2}{\text{m/sec}} \cr & {\text{Total}}\, {\text{distance}}\, {\text{to}}\, {\text{be}}\, {\text{covered}} \cr & = \left( {360 + 140} \right)m = 500\, m \cr & {\text{Formula}}\, {\text{for}}\, {\text{finding}}\, {\text{Time}} \cr & = \left( {\frac{{{\text{Distance}}}}{{{\text{Speed}}}}} \right) \cr & \therefore {\text{Required}}\, {\text{time}} \cr & = \left( {\frac{{500 \times 2}}{{25}}} \right)\, \sec \cr & = 40\, \sec . \cr\end{align}
Question 33 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Train A traveling at 63 kmph can cross a platform 199.5 m long in 21 seconds. How much would train A take to completely cross (from the moment they meet ) train B, 157 m long and traveling at 54 kmph in opposite direction which train A is traveling? (in seconds)
18 | |
16 | |
12 | |
10 |
Question 33 Explanation:
\begin{align} & {\text{Speed of train A}} \cr & {\text{ = 63 kmph}} \cr & {\text{ = }}\left( {\frac{{63 \times 5}}{{18}}} \right){\text{m/sec}} \cr & {\text{ = 17}}{\text{.5 m/sec}} \cr & {\text{Speed of train B}} \cr & {\text{ = 54 kmph}} \cr & {\text{ = }}\left( {\frac{{54 \times 5}}{{18}}} \right){\text{m/sec = 15 m/sec}} \cr & {\text{If the length of train A be }}x{\text{ metre, }} \cr & {\text{then}} \cr & {\text{Speed of train A}} \cr & {\text{ = }}\frac{{{\text{Length of train + length of platform}}}}{{{\text{Time taken in crossing}}}}{\text{ }} \cr & \Rightarrow 17.5 = \frac{{x + 199.5}}{{21}} \cr & \Rightarrow 17.5 \times 21 = x + 199.5 \cr & \Rightarrow 367.5 = x + 199.5 \cr & \Rightarrow x = 367.5 - 199.5 \cr & \Rightarrow 168\, {\text{metres}} \cr & {\text{Relative speed}} \cr & {\text{ = ( Speed train A + Speed train B)}} \cr & {\text{ = (17}}{\text{.5 + 15) m/sec}} \cr & {\text{ = 32}}{\text{.5 m/sec}} \cr & {\text{Required time}} \cr & {\text{ = }}\frac{{{\text{ Length of train A + Length of train B}}}}{{{\text{Relative speed }}}} \cr & = \left( {\frac{{168 + 157}}{{32.5}}} \right){\text{seconds}} \cr & = 10\, {\text{seconds}} \cr\end{align}
Question 34 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
72 | |
36 | |
18 | |
10 |
Question 34 Explanation:
\begin{align} & {\text{Let}}\, {\text{the}}\, {\text{speed}}\, {\text{of}}\, {\text{each}}\, {\text{train}}\, {\text{be}}\, x\, {\text{m/sec}}. \cr & {\text{Then, }}\, {\text{relative}}\, {\text{speed}}\, {\text{of}}\, {\text{the}}\, {\text{two}}\, {\text{trains}} = 2x\, {\text{m/sec}} \cr & {\text{So}}, \, 2x = \frac{{\left( {120 + 120} \right)}}{{12}} \cr & \Rightarrow 2x = 20 \cr & \Rightarrow x = 10 \cr & \therefore {\text{Speed}}\, {\text{of}}\, {\text{each}}\, {\text{train}} = 10\, {\text{m/sec}} \cr & = \left( {10 \times \frac{{18}}{5}} \right)\, {\text{km/hr}} = 36\, {\text{km/hr}} \cr\end{align}
Question 35 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Two trains are coming from opposite directions with speed of 75 km/hr and 100 km/hr on to parallel tracks. At some moment the distance between them is 100km. After T hours, distance between them is again 100 km. T is equal to?
17/2 hr | |
2 hr | |
11/2 hr | |
1 hr |
Question 35 Explanation:
\begin{align} & {\text{Relative speed}} \cr & {\text{ = (75 + 100)km/hr}} \cr & {\text{ = 175 km/hr}} \cr & {\text{Time taken to cover 175 km}} \cr & {\text{at relative speed = 1 hr}} \cr & \therefore {\text{T = Time taken to cover 200 km}} \cr & {\text{ = }}\left( {\frac{1}{{175}} \times 200} \right)hr \cr & = \frac{8}{7}\, hr \cr & = 1\frac{1}{7}hr \cr\end{align}
There are 35 questions to complete.