A wheel makes 2000 revolutions in covering a distance of 44 km. Find the radius of the wheel. MCQ with Answer and Explanation
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Question #1
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The speed index tracking profile of an express locomotive is exactly 20% higher than a commercial car. Both take off from terminal M together and reach terminal N, 120 km away, at the same instant. On the corridor route, the train logs a total stall of 10 minutes at intermediate stations. Find the car speed.
Correct Answer: Option C
Explanation:
Let car speed be c, then train tracking speed is 1.2c. Time difference parameter = 120/c - 120/(1.2c) = 10/60 hours = 1/6 hours. 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.
Let car speed be c, then train tracking speed is 1.2c. Time difference parameter = 120/c - 120/(1.2c) = 10/60 hours = 1/6 hours. 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.
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Time Speed and Distance
Question #2
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A car driver leaves Bangalore at 8:30 AM and expects to reach a place 300 km away at 12:30 PM. At 10:30 AM he finds that he has covered only 40% of the distance. By how much must he increase the speed of the car to reach on scheduled time?
Correct Answer: Option A
Explanation:
Total time available = 4 hours. At 10:30 AM (after 2 hours), distance covered = 40% of 300 = 120 km. Remaining distance = 180 km. Remaining time = 12:30 PM - 10:30 AM = 2 hours. Required speed = 180 / 2 = 90 km/h. Original speed = 120 / 2 = 60 km/h. Increase in speed = 90 - 60 = 30 km/h.
Total time available = 4 hours. At 10:30 AM (after 2 hours), distance covered = 40% of 300 = 120 km. Remaining distance = 180 km. Remaining time = 12:30 PM - 10:30 AM = 2 hours. Required speed = 180 / 2 = 90 km/h. Original speed = 120 / 2 = 60 km/h. Increase in speed = 90 - 60 = 30 km/h.
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Time Speed and Distance
Question #3
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A thief escapes from police custody at 1:00 PM running at 45 km/h. The police discover the escape at 1:20 PM and start chasing him at 60 km/h. At what time will the police catch the thief?
Correct Answer: Option B
Explanation:
In 20 minutes (1/3 hour), the thief covers 45 * (1/3) = 15 km. Relative speed = 60 - 45 = 15 km/h. Time taken to catch = 15 / 15 = 1 hour. Catching time = 1:20 PM + 1 hour = 2:20 PM.
In 20 minutes (1/3 hour), the thief covers 45 * (1/3) = 15 km. Relative speed = 60 - 45 = 15 km/h. Time taken to catch = 15 / 15 = 1 hour. Catching time = 1:20 PM + 1 hour = 2:20 PM.
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Maths
Time Speed and Distance
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