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Two trains, Calcutta Mail and Bombay Mail, start at the same time from stations Kolkata and Mumbai respectively towards each other. After passing each other, they take 12 hours and 3 hours to reach Mumbai and Kolkata respectively. If the Calcutta Mail is moving at the speed of 48 km/h, the speed of the Bombay Mail is
- a)24 km/h
- b)22 km/h
- c)21 km/h
- d)96 km/h
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Two trains, Calcutta Mail and Bombay Mail, start at the same time from...
If you assume that the initial stretch of track is covered by the two trains in time t each, the following figure will give you a clearer picture.
From the above figure, we can deduce that, t/3 = 12/t.
Hence, t2 = 36, gives us t = 6.
Hence, the distance between Kolkata to the starting point is covered by the Calcutta Mail in 6 hours, while the same distance is covered by the Bombay Mail in 3 hours.
Hence, the ratio of their speeds would be 1:2. Hence, the Bombay Mail would travel at 96 kmph.
From the above figure, we can deduce that, t/3 = 12/t.
Hence, t2 = 36, gives us t = 6.
Hence, the distance between Kolkata to the starting point is covered by the Calcutta Mail in 6 hours, while the same distance is covered by the Bombay Mail in 3 hours.
Hence, the ratio of their speeds would be 1:2. Hence, the Bombay Mail would travel at 96 kmph.
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Community Answer
Two trains, Calcutta Mail and Bombay Mail, start at the same time from...
Given:
- Speed of Calcutta Mail = 48 km/h
- Time taken by Calcutta Mail to reach Kolkata after passing Bombay Mail = 12 hours
- Time taken by Bombay Mail to reach Mumbai after passing Calcutta Mail = 3 hours
To find:
- Speed of Bombay Mail
Concept:
- The relative speed of two objects moving towards each other is the sum of their individual speeds.
- We can use the formula: Distance = Speed x Time.
Assumption:
- Let the distance between Kolkata and Mumbai be D km.
Calculation:
- Let the speed of Bombay Mail be x km/h.
- Calcutta Mail travels for 12 hours to reach Kolkata, so the distance traveled by Calcutta Mail = Speed x Time = 48 x 12 = 576 km.
- Bombay Mail travels for 3 hours to reach Mumbai, so the distance traveled by Bombay Mail = Speed x Time = x x 3 = 3x km.
- When they pass each other, the sum of the distances traveled by both trains is equal to the total distance between Kolkata and Mumbai: 576 + 3x = D.
- We also know that the time taken by Bombay Mail to reach Kolkata after passing Calcutta Mail is 12 hours.
- So, the distance traveled by Bombay Mail = Speed x Time = x x 12 = 12x km.
- Since the total distance traveled by Bombay Mail is the same in both cases, we can equate the two distances: 3x = 12x.
- Solving this equation, we get x = 96 km/h.
Conclusion:
- The speed of the Bombay Mail is 96 km/h. Hence, the correct answer is option D.
- Speed of Calcutta Mail = 48 km/h
- Time taken by Calcutta Mail to reach Kolkata after passing Bombay Mail = 12 hours
- Time taken by Bombay Mail to reach Mumbai after passing Calcutta Mail = 3 hours
To find:
- Speed of Bombay Mail
Concept:
- The relative speed of two objects moving towards each other is the sum of their individual speeds.
- We can use the formula: Distance = Speed x Time.
Assumption:
- Let the distance between Kolkata and Mumbai be D km.
Calculation:
- Let the speed of Bombay Mail be x km/h.
- Calcutta Mail travels for 12 hours to reach Kolkata, so the distance traveled by Calcutta Mail = Speed x Time = 48 x 12 = 576 km.
- Bombay Mail travels for 3 hours to reach Mumbai, so the distance traveled by Bombay Mail = Speed x Time = x x 3 = 3x km.
- When they pass each other, the sum of the distances traveled by both trains is equal to the total distance between Kolkata and Mumbai: 576 + 3x = D.
- We also know that the time taken by Bombay Mail to reach Kolkata after passing Calcutta Mail is 12 hours.
- So, the distance traveled by Bombay Mail = Speed x Time = x x 12 = 12x km.
- Since the total distance traveled by Bombay Mail is the same in both cases, we can equate the two distances: 3x = 12x.
- Solving this equation, we get x = 96 km/h.
Conclusion:
- The speed of the Bombay Mail is 96 km/h. Hence, the correct answer is option D.
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Two trains, Calcutta Mail and Bombay Mail, start at the same time from stations Kolkata and Mumbai respectively towards each other. After passing each other, they take 12 hours and 3 hours to reach Mumbai and Kolkata respectively. If the Calcutta Mail is moving at the speed of 48 km/h, the speed of the Bombay Mail isa)24 km/hb)22 km/hc)21 km/hd)96 km/hCorrect answer is option 'D'. Can you explain this answer?
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