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Arithmetic: Time Speed Distance Test-9

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Question 1
Two trains are running with speed 30 km/hr. and 58km/hr. in the same directions. A man in the slower train passes the faster train in 18 seconds. The length (in metres) of the faster trains is:
A
70
B
100
C
128
D
140
Question 1 Explanation: 
The relative speed = 58-30 = 28 Km/hr. =140/18 m/s.
Therefore in 18 secs the faster train travels =$ \frac{140}{18}\times 18=140m$
Question 2
Two trains travel in the same direction at the speeds of 56km/hr. and 29km/hr. respectively. The faster train passes a man in the slower trains in 10 seconds. The length of the faster train (in metres) is
A
100
B
80
C
75
D
120
Question 2 Explanation: 
The relative speed is 56-29 Km/hr =$ \frac{27}{18}\times 5=7.5m/s$
The faster train travels only the length of it’s own = 7.5 x 10 = 75 m.
Question 3
A bus moving at a speed of 45 km/hr. overtakes a truck 150 metres ahead going in the same directions in 30 seconds. The speed of the truck is
A
27km/hr.
B
24km/hr.
C
25km/hr.
D
28km/hr.
Question 3 Explanation: 
The lag of 150 m has been covered by the bus in 30 seconds.
Therefore, the relative speed of the bus and truck is =$ \displaystyle \frac{5\times 18}{5}=18km/h$
The speed of truck is 45-18 = 27 Km/hr.
Question 4
Two trains of equal length are running on parallel lines in the same directions at 46km/hr. and 36km/hr. The faster trains pass the slower train in 36 seconds. The length of each train is:
A
82m
B
50m
C
72m
D
80m
Question 4 Explanation: 
The relative speed of train is 46-36 = 10 Km/hr =$ \frac{10\times 5}{18}=\frac{25}{9}m/s$
In 36 secs the total distance travelled is 36x25/9 = 100 m.
Therefore the length of each train is = 100/2 = 50 m.
Question 5
Two trains start from a certain place on two parallel tracks in the same directions. The speed of the trains are 45km/hr. and 40km/hr. respectively. The distance between the two trains after 45 minutes will be
A
2 km 500 m
B
2 km 750 m
C
3 km 750 m
D
3 km 250 m
Question 5 Explanation: 
In one hour the distance between the trains is 5 km.
In 45 mins = ¾ hour the distance would be equal to  ¾ X 5
= 3.75 Km = 3 Km 750 m.
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