A person has to cover a distance of 160 km. He covers the first half of the distance at 40 km/h. At what speed must he travel the remaining half to make the average speed for the whole journey 50 km/h? MCQ with Answer and Explanation
A person has to cover a distance of 160 km. He covers the first half of the distance at 40 km/h. At what speed must he travel the remaining half to make the average speed for the whole journey 50 km/h?
A. 60 km/h
B. 75 km/h
C. 70 km/h
D. 66.67 km/h
Answer: Option D
Solution (By JKSSB Mock Tests)
Let the required speed for the second half be x km/h. Using the average speed formula for equal halves: Average Speed = 2v1*v2 / (v1 + v2) => 50 = (2 * 40 * x) / (40 + x) => 50(40 + x) = 80x => 2000 + 50x = 80x => 30x = 2000 => x = 66.67 km/h.
A train 200 meters long passes a running man in 10 seconds when both move in the same direction. If the speed of the man is 6 km/h, find the speed of the train.
Explanation:
Relative speed = 200 / 10 = 20 m/s = 20 * (18/5) = 72 km/h. In the same direction, Relative Speed = Speed of train - Speed of man => 72 = Speed of train - 6 => Speed of train = 78 km/h.
A train passing a stationary pole takes 8 seconds, and it requires 20 seconds to completely pass a 240-meter long platform. Find the speed of the train in km/h.
Explanation:
Time taken to cross the platform distance alone = 20 - 8 = 12 seconds. Speed of train = 240 / 12 = 20 m/s. In km/h = 20 * (18/5) = 72 km/h.
A vehicle covers a specific highway distance at 50 km/h. If it spikes its speed to 60 km/h, it clears the stretch 20 minutes early. Find the total distance.
Explanation:
Time difference = 20 minutes = 20/60 = 1/3 hours. Let distance be d. d / 50 - d / 60 = 1/3 => (6d - 5d) / 300 = 1/3 => d / 300 = 1/3 => d = 100 km.
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