A contract courier can travel at 40 km/h to deliver a package on time. If he travels at 30 km/h, he is late by 2 hours. What is the distance he has to cover? MCQ with Answer and Explanation
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Question #1
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A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30 km upstream and 21 km downstream in 6 hours 30 minutes. Find the speed of the boat in still water.
Correct Answer: Option D
Explanation:
Let 1/u = x and 1/d = y. 24x + 28y = 6 and 30x + 21y = 6.5. Solving these linear equations gives x = 1/6 and y = 1/14. So upstream speed u = 6 km/h, downstream speed d = 14 km/h. Speed in still water = (d + u)/2 = (14 + 6)/2 = 10 km/h.
Let 1/u = x and 1/d = y. 24x + 28y = 6 and 30x + 21y = 6.5. Solving these linear equations gives x = 1/6 and y = 1/14. So upstream speed u = 6 km/h, downstream speed d = 14 km/h. Speed in still water = (d + u)/2 = (14 + 6)/2 = 10 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 D
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 train passes a 150-meter long bridge in 15 seconds and a standard sign post in 9 seconds. Find the length of the train.
Correct Answer: Option A
Explanation:
Time taken to cross the bridge alone = 15 - 9 = 6 seconds. Speed of train = 150 / 6 = 25 m/s. Length of train = Speed * Time to cross sign post = 25 * 9 = 225 meters.
Time taken to cross the bridge alone = 15 - 9 = 6 seconds. Speed of train = 150 / 6 = 25 m/s. Length of train = Speed * Time to cross sign post = 25 * 9 = 225 meters.
This question belongs to:
Maths
Time Speed and Distance
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