Question : A policeman noticed a thief from 300 m. The thief started running and the policeman was chasing him. The thief and the policeman ran at speeds of 8 km/h and 9 km/h, respectively. What was the distance between them after 3 minutes?
Option 1: 225 m
Option 2: 250 m
Option 3: 300 m
Option 4: 200 m
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Correct Answer: 250 m
Solution : Given: Distance between the policeman and the thief = 300 m Speed of the policeman = 9 km//h = $9×\frac{5}{18}=\frac{5}{2}$ m/s Speed of the thief = 8 km//h = $8×\frac{5}{18}=\frac{20}{9}$ m/s Relative speed of the policeman and the thief = 9 – 8 = 1 km/h = $1×\frac{5}{18}=\frac{5}{18}$ m/s Gap reduced after 3 minutes = $\frac{5}{18}×180$ = 50 m The distance between them after 3 minutes = 300 – 50 = 250 m Hence, the correct answer is 250 m.
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Question : A thief steals an item and escapes, running at a speed of 15 km/h. A policeman arrives at the spot of the crime after 4 minutes and immediately starts chasing the thief. 16 minutes after the policeman started to chase the thief, there was still a gap of 200 m between the two. At what distance from the spot of the crime will the policeman catch up with the thief and what is the speed of the policeman?
Option 1: 5.5 km; 16.5 km/h
Option 2: 6 km; 18 km/h
Option 3: 6.5 km; 19.5 km/h
Option 4: 5 km; 15 km/h
Question : A thief is noticed by a policeman from a distance of 500 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rates of 17 km/hr and 20 km/hr, respectively. What is the distance between them after 8 minutes?
Option 1: 100 m
Option 2: 180 m
Option 3: 200 m
Option 4: 150 m
Question : A policeman follows a thief, who is 1250 m ahead of him. The policeman and the thief run at speeds of 10 km/h, and 8 km/ h respectively. The distance (in km) run by the thief before he is nabbed by the policeman is:
Option 1: 7 km
Option 2: 4 km
Option 3: 5 km
Option 4: 6 km
Question : A policeman saw a thief from a distance of 450 m. When the policeman started chasing him, the thief also started running. The ratio of speeds of the thief to the policeman is 7 : 8. After running how much distance (in km) can the policeman catch the thief?
Option 1: 3.75
Option 2: 3.4
Option 3: 3.6
Option 4: 3.15
Question : A thief steals an item and escapes, running at 20 km/hr. A policeman arrives at the spot of the crime after 6 minutes and immediately starts chasing the thief. 24 minutes after the policeman started to chase the thief, there is still a gap of 400 m between the two. At what distance from the spot of crime would the policeman catch up with the thief and what is the speed at which the policeman ran?
Option 1: 15 km; 25 km/hr
Option 2: 14.4 km; 24 km/hr
Option 3: 10 km; 25 km/hr
Option 4: 12 km; 24 km/hr
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