The speed of a train is 20% more than the speed of a car. Both start from city P at the same time and reach city Q, 120 km away, at the same time. On the way, the train stops for 10 minutes at various stations. What is the speed of the car? MCQ with Answer and Explanation
The speed of a train is 20% more than the speed of a car. Both start from city P at the same time and reach city Q, 120 km away, at the same time. On the way, the train stops for 10 minutes at various stations. What is the speed of the car?
A. 100 km/h
B. 150 km/h
C. 120 km/h
D. 140 km/h
Answer: Option C
Solution (By JKSSB Mock Tests)
Let car speed be c, then train speed is 1.2c. Time difference = 120/c - 120/(1.2c) = 10/60 hour = 1/6 hour. 120/c * (1 - 1/1.2) = 1/6 => 120/c * (0.2/1.2) = 1/6 => 120/c * (1/6) = 1/6 => c = 120 km/h.
Explanation:
Let speed of current be c. 24 / (9 + c) + 24 / (9 - c) = 6. Dividing by 6: 4 / (9 + c) + 4 / (9 - c) = 1 => 4(9 - c + 9 + c) = 81 - c^2 => 72 = 81 - c^2 => c^2 = 9 => c = 3 km/h.
The speed indices of two sprinters are in the ratio 3 : 4. If the first sprinter requires 24 seconds to wrap up a bend, how much time does the second sprinter require?
Explanation:
Ratio of speeds = 3:4, so ratio of times required = 4:3. Given 4 parts = 24 seconds => 1 part = 6 seconds. Time for the second sprinter = 3 parts = 3 * 6 = 18 seconds.
Explanation:
Relative speed = 125 / 10 = 12.5 m/s = 12.5 * (18/5) = 45 km/h. Since they are in the same direction: Relative Speed = Speed of train - Speed of man => 45 = Speed of train - 5 => Speed of train = 50 km/h.
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