Question : A thief, seeing a policeman from a distance of 120 m, starts running at a speed of 7 km/hr. The policeman chases immediately with a speed of 8 km/hr and the thief is caught. What is the distance run by the thief?
Option 1: 820 m
Option 2: 780 m
Option 3: 840 m
Option 4: 800 m
Correct Answer: 840 m
Solution : The relative speed of the policeman and the thief = 8 – 7 = 1 km/hr = 1 × $\frac{5}{18}$ m/s = $\frac{5}{18}$ m/s The time it takes for the policeman to catch the thief = $\frac{120}{\frac{5}{18}}$ = 432 s The speed of the thief = 7 km/hr = 7 × $\frac{5}{18}$ m/s = $\frac{35}{18}$ m/s $\therefore$ The distance run by the thief = $\frac{35}{18}$ × 432 = 840 m Hence, the correct answer is 840 m.
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Question : A thief is spotted by a policeman from a distance of 250 m. When the policeman starts the chase, the thief also starts running. Assuming that the speed of the thief is 10 km/h and that of the policeman is 12 km/h, how far would the thief have run before he is caught?
Option 1: 4 km
Option 2: 1.25 km
Option 3: 3 km
Option 4: 2 km
Question : A policeman sees a thief at a distance of 150 m. He starts chasing the thief who is running at a speed of 5 m/sec, while the policeman chases with a speed of 7 m/sec. Find the distance covered by the thief when he is caught by the policeman.
Option 1: 285 m
Option 2: 325 m
Option 3: 375 m
Option 4: 295 m
Question : A thief is noticed by a policeman from a distance of 300 m. The thief starts running and the policeman starts chasing him. The thief and policeman run at the rate of 11 km/hr and 13 km/hr, respectively. After running for how many kilometres will the policeman be able to catch the thief?
Option 1: 1.65
Option 2: 1.85
Option 3: 1.75
Option 4: 1.95
Question : A man covers a certain distance by bike. If he covers 25% of the distance at the speed of 25 km/hr, 50% of the distance at the speed of 50 km/hr and the remaining distance at the speed of 12.5 km/hr, find his average speed over the whole journey.
Option 1: 20 km/hr
Option 2: 30 km/hr
Option 3: 25 km/hr
Option 4: 35 km/hr
Question : During a journey of 120 km, Rahi drives the first 60 km at the speed of 60 km/hr, the next 30 km at 60 km/hr and the remaining 30 km at the speed of 30 km/hr. Determine the average speed.
Option 1: 48 km/hr
Option 2: 33.33 km/hr
Option 3: 50 km/hr
Option 4: 40 km/hr
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