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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:
A
990 km
B
1200 km
C
1320 km
D
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
A
100 km./hr.
B
120 km./hr.
C
140 km./hr.
D
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
A
14.4 seconds
B
15.5 seconds
C
18.8 seconds
D
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
A
8 seconds.
B
6 seconds
C
7 seconds
D
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
A
45km./hr.
B
48km./hr.
C
52km./hr.
D
54km./hr.
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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