Question : A thief is noticed by a policeman from a distance of 150 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 8 km/hr and 10 km/hr respectively. At what distance will the policeman catch the thief?
Option 1: 1000 metres
Option 2: 850 metres
Option 3: 500 metres
Option 4: 750 metres
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Correct Answer: 750 metres
Solution : The relative speed of policeman to the thief = (10 – 8) = 2 km/hr = $\frac{2×5}{18}$ = $\frac{5}{9}$ m/s The time taken by the police to catch the thief = $150\div\frac{5}{9}$ = 270 seconds Now, the speed of the policeman = 10 km/hr = $\frac{10×5}{18}$ = $\frac{25}{9}$ m/s So, the distance travelled by the policeman in 270 seconds = $\frac{25}{9}×270$ = 750 metres Hence, the correct answer is 750 metres.
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Question : A policeman spots a thief at a distance of 200 m and starts chasing him. While the policeman runs at a speed of 9 km/hr, the thief runs at a speed of 7 km/hr. After how long will the policeman catch the thief?
Option 1: 6 minutes
Option 2: 3 minutes
Option 3: 10 minutes
Option 4: 5 minutes
Question : Two trains 100 metres and 95 metres long, respectively pass each other in 27 seconds when they run in the same direction and in 9 seconds when they run in opposite directions. The speeds of the two trains are:
Option 1: 44 km/hr, 22 km/hr
Option 2: 52 km/hr, 26 km/hr
Option 3: 36 km/hr, 18 km/hr
Option 4: 40 km/hr, 20 km/hr
Question : A 1000-metre-long train is running at the speed of 72 km/hr. If it crosses a bridge in 85 seconds, then what is the length of the bridge?
Option 1: 800 metres
Option 2: 700 metres
Option 3: 950 metres
Question : A walks at a speed of 10 km/hr and 20 hours after his start, B starts on his cycle after him at the speed of 15 km/hr. How far from the starting point will B catch A?
Option 1: 600 km
Option 2: 800 km
Option 3: 1000 km
Option 4: 700 km
Question : A man starts from place A and reaches place B in 50 hours. He travels $\frac{1}{4}$th distance at the speed of 5 km/hr and the remaining distance at the speed of 15 km/hr. What is the distance between A and B?
Option 1: 525 km
Option 2: 500 km
Option 3: 375 km
Option 4: 425 km
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