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Arithmetic: Time Speed Distance Test-8

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Question 1
Two trains start from stations A and B and travel towards each other at speeds of 50 km/hour and 60 km/hour respectively. At the time of their meeting, the second train has travelled 120 km more than the first. The distance between A and B is:
990 km
1200 km
1320 km
1440 km
Question 1 Explanation: 
The speed of B is 10 Km/hr more than A.
Therefore the difference of 120 km must have been created in =120/10 = 12 hrs.
The relative speed = 110 Km/hr.
The total distance is 110 km/hr X 12 = 1320 Km
Correct option is (c).
Question 2
Two trains are moving on two parallel tracks but in opposite directions. A person sitting in the train moving at the speed of 80 km/hr passes the second train in 18 seconds. If the length of the seconds train is 1000m, its speed is
100 km./hr.
120 km./hr.
140 km./hr.
150 km./hr.
Question 2 Explanation: 
We have to consider the negligible distance contributed by the 1st train
as only the man is to be considered.
Therefore, 1000 m is to be traveled in 18 sec.
speed in km/hr is (1000/18) x (18/5) = 200km/h This is the relative speed of two trains.
Therefore the speed of 2nd train is 200-80 = 120 Km/h
Question 3
Two trains of equal length, running in opposite directions, passes pole in 18 and 12 seconds. The trains will cross each other in
14.4 seconds
15.5 seconds
18.8 seconds
20.2 seconds
Question 3 Explanation: 
Let the length be x m.
total length = 2x m
Speed of one train is x/18 m/s and x/12 m/s.
Total time isĀ  =$ \displaystyle \frac{2x}{\frac{x}{18}+\frac{x}{12}}=14.4\sec $
Question 4
Two trains 105 metres and 90 metres long, run at the speeds of 45 km/hr and 72km/hr respectively, in opposite directions on parallel tracks. The time which they take to cross each other, is
8 seconds.
6 seconds
7 seconds
5 seconds
Question 4 Explanation: 
Let the train with length 105 m be marked as A and the second train of length 90m be marked as B..
Speed of A: 45 x 5/18= 25/3 m/s
Speed of B: 72 x 5/18= 20 m/s.
Relative speed = 25/3+20 = 85/3 m/s
Total distance = 195 m
therefore the time taken is
$ \frac{195}{(72+45)\times \frac{5}{18}}=6\sec $
Question 5
A train, 150m long, passes a pole in 15 seconds and another train of the same length travelling in the opposite direction in 12 seconds. The speed of the seconds train is
Question 5 Explanation: 
Speed of the first train is 150m/15 secs = 10 m/s.
In 12 sec it covers 120 m.
Now the actual distance to cross the train is 150 +150 =300 m.
Therefore the second train travels at 300 -120 = 180 m in 12 secs.
Speed of 2nd train is 15 m/s. = 15 x 18 /5 = 54 Km /hr.
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