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After travelling a certain distance, a train develops a snag and its speed is decreased to half of its original speed and thus, it reaches its destination 45 minutes late. Had the snag occurred 30 km further, it would have reached its destination 15 minutes earlier. What is the speed of the train?
- a)90 kmph
- b)105 kmph
- c)150 kmph
- d)120 kmph
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
After travelling a certain distance, a train develops a snag and its ...
Problem Statement:
A train develops a snag and its speed is decreased to half of its original speed and thus, it reaches its destination 45 minutes late. Had the snag occurred 30 km further, it would have reached its destination 15 minutes earlier. What is the speed of the train?
Solution:
Let's assume the distance traveled by the train is 'd', and its original speed is 's'.
1. First Case:
In the first case, the train reaches its destination 45 minutes late, so the time taken by the train to cover the distance 'd' is given by
t1 = d/s + 45/60
2. Second Case:
In the second case, if the snag occurred 30 km further, the distance traveled by the train would be 'd+30'. Also, it would have reached its destination 15 minutes earlier, so the time taken by the train to cover the distance 'd+30' is given by
t2 = (d+30)/s*2 - 15/60
3. Equating the Time Taken:
As per the problem, the time taken in the first and second cases should be equal. Therefore, we can equate t1 and t2 and solve for 's'.
d/s + 45/60 = (d+30)/s*2 - 15/60
2d + 90 = (d+30)*2/s
s = 120 kmph
Hence, the speed of the train is 120 kmph.
A train develops a snag and its speed is decreased to half of its original speed and thus, it reaches its destination 45 minutes late. Had the snag occurred 30 km further, it would have reached its destination 15 minutes earlier. What is the speed of the train?
Solution:
Let's assume the distance traveled by the train is 'd', and its original speed is 's'.
1. First Case:
In the first case, the train reaches its destination 45 minutes late, so the time taken by the train to cover the distance 'd' is given by
t1 = d/s + 45/60
2. Second Case:
In the second case, if the snag occurred 30 km further, the distance traveled by the train would be 'd+30'. Also, it would have reached its destination 15 minutes earlier, so the time taken by the train to cover the distance 'd+30' is given by
t2 = (d+30)/s*2 - 15/60
3. Equating the Time Taken:
As per the problem, the time taken in the first and second cases should be equal. Therefore, we can equate t1 and t2 and solve for 's'.
d/s + 45/60 = (d+30)/s*2 - 15/60
2d + 90 = (d+30)*2/s
s = 120 kmph
Hence, the speed of the train is 120 kmph.
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Community Answer
After travelling a certain distance, a train develops a snag and its ...
If we think carefully, we may conclude that the speed of the train up to a certain distance is the same in both the cases and also, the speed after the distance of 30 km further is the same in both the cases. Thus, the difference in time, i.e. 15 minutes, is only due to the difference in speed for the 30 km journey.
Now, if the speed of the train is x km/h, then
x = 120 kmph
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