A thief who is chased by the police escaped in a bike at 36 km/hr. After thief covered a distance of 500 m, the police start chasing him with a speed of 54 km/hr. Every time the police reaches the thief, the thief doubles his speed for 10 seconds and revert back to the original speed. After the end of 4 min, the bike stops because of empty fuel tank. If the mileage of the bike is 29 kmpl, how much fuel was there in the bike before starting (in ml)? Correct Answer 124 Initially they were 500 m apart, both were moving at a speed of 54 km/hr and 36 km/hr i.e. 15 m/s and 10 m/s ⇒ Relative speed of thief and police = 15 – 10 = 5 m/s ⇒ Time taken for them to meet = Relative displacement/Relative speed = 500/5 = 100 sec ⇒ Distance covered by thief in 100 sec = Speed of the thief × 100 = 10 × 100 = 1000 m Now thief doubles the speed for 10 sec For the next 10 second, his speed will be 20 m/s ⇒ Distance covered by thief in 10 sec = Speed of the thief × 10 = 20 × 10 = 200 m In 10 sec, police would have travelled only 10× 15 = 150 m Now they will be 50 m apart and the thief reverts back to same speed. ⇒ Relative speed of thief and police = 15 – 10 = 5 m/s ⇒ Time taken for them to meet = Relative displacement/Relative speed = 50/5 = 10 sec ⇒ Distance covered by thief in 10 sec = Speed of the thief × 10 = 10 × 10 = 100 m After that the cycle repeats. So, every 20 sec they will meet each other and by that time the thief would have covered 300 m Total amount of time = 100 + n × 20 , where n = number of cycles. ⇒ 4 × 60 = 100 + 20n ⇒ n = 7 Total distance covered = initial separation + 1000 m + n × 200 = 500 + 1000 + 300 × 7 = 3600 m = 23.6 km ∴ Amount of fuel = Distance covered/ mileage = 3.6/29 = 0.124 L = 124 ml