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
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Correct Answer: 6 km; 18 km/h
Solution : Distance travelled by thief before police started chasing him = 15 × $\frac{4}{60}$ = 1 km Distance travelled by the thief in 16 minutes after police started chasing him = 15 × $\frac{16}{60}$ = 4 km In 16 minutes, the gap between the thief and the policeman will be reduced by = 1000 - 200 = 800 m So, the remaining gap of 200 m will be covered in = $\frac{200}{800}$ × 16 = 4 minutes $\therefore$ Distance covered by thief in 4 minutes = $15\times\frac{4}{60}$ = 1 km Hence, total distance covered by thief before getting caught = 1 + 4 + 1 = 6 km Now, the speed of the policeman = $\frac{\text{Distance}}{\text{Time}} = \frac{6\ \mathrm{km} \times60}{(16+4)\ \mathrm{hr}}$ = 18 km/h Hence, the correct answer is '6 km, 18 km/h'.
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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
Question : A thief seeing a policeman from a distance of 300 m starts running at a speed of 10 km/h. The policeman gives chase immediately at a speed of 12 km/h and the thief is caught. What is the distance run by the thief?
Option 1: 2 km
Option 2: 2.5 km
Option 3: 3.2 km
Option 4: 1.5 km
Question : A policeman saw a thief at a distance of 400 m. The thief started running at a speed of 10 km/h and the policeman chased him at 12 km/h in the same direction. At what distance from the starting point will the policeman catch the thief?
Option 1: 2.4 km
Option 2: 3 km
Option 3: 2 km
Option 4: 2.8 km
Question : A thief steals a van at 3:00 a.m. and drives it at a speed of 57 km/h. The thief is discovered at 4:00 a.m. and the owner starts chasing in another van, at a speed of 76 km/h. At what time will he catch the thief?
Option 1: 7:30 a.m.
Option 2: 7:00 p.m.
Option 3: 7:00 a.m.
Option 4: 6:00 a.m.
Question : A policeman spots a thief at a distance of 360 m. Both the policeman and the thief simultaneously start running, with the former chasing the latter. While the thief runs at the speed of 8 km/h, the policeman runs at 9.2 km/h. How many metres will the policeman have to run before he catches up with the thief?
Option 1: 2852
Option 2: 2714
Option 3: 2668
Option 4: 2760
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