Question : A thief is spotted by a policeman from a distance of 210 m. When the policeman starts the chase, the thief also starts running. If the speed of the thief is 25 km/hr and that of the policeman is 32 km/hr, then how far would the thief have run (in m) before he is overtaken?
Option 1: 920
Option 2: 480
Option 3: 1200
Option 4: 750
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Correct Answer: 750
Solution : Let the time taken to catch the thief be $x$ hour. Distance travelled by thief going at 25 km/hr = $25x$ Distance travelled by policeman going at 32 km/hr = $32x$ Now, distance travelled by thief + $\frac{210}{1000}$ = Distance travelled by policeman ⇒ $25x + \frac{210}{1000} = 32x$ ⇒ $x = \frac{30}{1000}$hours Distance travelled by thief going at 25 km/hours $=25x=25\times \frac{30}{1000}=\frac{3}{4}$ km $=$ 750 m Hence, the correct answer is 750.
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Question : A thief is stopped by a policeman from a distance of 150 metres. When the policeman starts the chase, the thief also starts running. Assuming the speed of the thief is 7 km/h and that of the policeman is 9 km/h, how far would the thief have run before he was overtaken by the policeman?
Option 1: 420 metres
Option 2: 630 metres
Option 3: 315 metres
Option 4: 525 metres
Question : A thief is spotted by a constable from 200 m. When the constable starts the chase, the thief also starts running. If the speed of the constable is 8 km/h and the thief runs at the speed of 6 km/h, then how far (in m) will the thief be able to run before he is overtaken?
Option 1: 600
Option 2: 400
Option 3: 550
Option 4: 500
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 thief running at a speed of ‘$x$’ km/hr is chased by a policeman running at a speed of 10 km/hr. If the thief is ahead by 100 metres, the policeman catches the thief after 3 minutes. At what speed is the thief running (‘$x$’ being the unknown speed)?
Option 1: 4 km/hr
Option 2: 8 km/hr
Option 3: 10 km/hr
Option 4: 6 km/hr
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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