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Arithmetic: Time Speed Distance Test-4

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Question 1
A thief is noticed by a policeman from a distance of 200m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
100 m
190 m
200 m
150 m
Question 1 Explanation: 
In every hour the policeman is gaining a speed of 11-10=1Km.
Therefore for 6 min the gain would be =$ \frac{1000}{60}\times 6=100$
The distance between them is 200 -100 = 100 m.
Question 2
A moving train, 66 metres long, overtakes another train of 88 metres long, moving in the same directions in 0.168 minutes. If the seconds train is moving at 30 km per hr, at what speed is the first train moving?
85 km/hr.
50 km/hr.
55 km/hr.
25 km/hr.
Question 2 Explanation: 
Total distance to be traveled to cross the other train is 66+88 = 154 m.
The time taken to travel is 0.168 min = 0.168 X 60 sec =10.8 sec
The relative speed is =$ \frac{154}{10}\times \frac{18}{5}=\frac{2772}{50}=55.44km/h$
Since they were moving in same direction,
Speed of 1st train – 30 = 55.44 ;
Speed of 1st train is 85.44 Km/hr.
Question 3
A constable is 114 meters behind a thief. The constable runs 21 metres and the thief 15 metres in a minute. In what time will the constable catch the thief?
19 minutes
18 minutes
17 minutes
16 minutes
Question 3 Explanation: 
For every minute the constable gains 21-15= 6 meters per minute.
To catch the thief constable has to gain 114 m.
Therefore the required time is =$ \frac{114}{6}=19\min $
Question 4
How much time does a train, 50m long, moving at 68 km/hour take to pass another train, 75m long, moving at 50 km/hour in the same direction?
5 seconds
10 seconds
20 seconds
25 seconds
Question 4 Explanation: 
Distance to be travelled is 50 m + 75 m = 125 m.
The relative speed = 68-50 = 18 km/hr =$ \displaystyle 18\times \frac{5}{18}=5m/s$
The time taken is 125 /5 s = 25 s.
Question 5
A constable follows a thief who is 200 m ahead of the constable. If the constable and the thief run at speeds of 8km/hour and 7 km/hour respectively, the constable would catch the thief in
10 minutes
12 minutes
15 minutes
20 minutes
Question 5 Explanation: 
The constable gains 8-7=1 km every hour over thief.
Therefore,the constable gains 5/18 m every sec.
To catch the thief the constable needs to gain =$ \frac{200}{5}\times 18=720\,\sec $
Time = 12 min.
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