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
Correct Answer: 1.25 km
Solution : Distance between the thief and the policeman = 250 m Speed of the thief = 10 km/h = $\frac{25}{9}$ m/s Speed of the policeman = 12 km/h = $\frac{10}{3}$ m/s The relative speed of the thief and the policeman = 12 – 10 = 2 km/h or 2 × $\frac{5}{18}$ = $\frac{5}{9}$ m/s Time taken by the policeman to catch the thief T = $\frac{250}{\frac{5}{9}}$ T = 50 × 9 = 450 s Now the distance travelled by the thief before getting caught D = $\frac{25}{9}$ × 450 D = 25 × 50 = 1250 m or 1.25 km ∴ The thief ran 1.25 km before he was caught. Hence, the correct answer is 1.25 km.
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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
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 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 car covered the first 100 km at a speed of 50 km/h. It covered the next 140 km at a speed of 70 km/h. What is its average speed?
Option 1: 60 km/h
Option 2: 62 km/h
Option 3: 58 km/h
Option 4: 64 km/h
Question : A bus starts running with an initial speed of 33 km/hr and its speed increases every hour by a certain amount. If it takes 7 hours to cover a distance of 315 km, what will be the hourly increment (in km/hr) in the speed of the bus?
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
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