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A train after travelling for a certain distance develops a problem and decreases its speed to half its original speed and reaches its destination 45 minutes late. Had the problem occurred 30 km further on, it would have reached its destination 15 minutes earlier. What is the speed of the train?
- a)30 km/ hr
- b)90km/h r
- c)120km/hr
- d)150km/hr
Correct answer is option 'A'. Can you explain this answer?
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A train after travelling for a certain distance develops a problem and...
Let A be the starting point and B is the destination. C and D are places where the problems occurred. Let the speed of the train is ‘x’ km/hr.
Most Upvoted Answer
A train after travelling for a certain distance develops a problem and...
Given:
Let the original speed of the train be x km/hr.
Let the distance travelled be y km.
Problem 1:
On developing a problem, the train decreases its speed to half.
New speed of the train = x/2 km/hr
Time taken to cover the distance y km at the new speed = y/(x/2) = 2y/x hours
The train reaches its destination 45 minutes late, which is equal to 3/4 hours.
Therefore, the time taken to cover the distance y km at the original speed = (2y/x) + 3/4 hours.
Problem 2:
Had the problem occurred 30 km further on, the train would have reached its destination 15 minutes earlier, which is equal to 1/4 hours.
Let the distance travelled before the problem occurred be z km.
Therefore, the distance travelled from the point where the problem occurred to the destination = (y - z) km.
New time taken to cover the distance (y - z) km at the new speed = (y - z)/(x/2) = 2(y - z)/x hours
The train reaches its destination 15 minutes earlier, which is equal to 1/4 hours.
Therefore, the time taken to cover the distance y km at the original speed = (2(y - z)/x) - 1/4 hours.
Equating the two expressions for the time taken to cover the distance y km at the original speed, we get:
(2y/x) + 3/4 = (2(y - z)/x) - 1/4
Simplifying, we get:
z = 30
Substituting this value in any one of the above expressions for time taken to cover the distance y km at the original speed, we get:
(2y/x) + 3/4 = (2(y - 30)/x) - 1/4
Simplifying, we get:
y = 120
Therefore, the speed of the train = x = (2y)/[(2y/x) + 3/4] = 30 km/hr.
Hence, option A is the correct answer.
Let the original speed of the train be x km/hr.
Let the distance travelled be y km.
Problem 1:
On developing a problem, the train decreases its speed to half.
New speed of the train = x/2 km/hr
Time taken to cover the distance y km at the new speed = y/(x/2) = 2y/x hours
The train reaches its destination 45 minutes late, which is equal to 3/4 hours.
Therefore, the time taken to cover the distance y km at the original speed = (2y/x) + 3/4 hours.
Problem 2:
Had the problem occurred 30 km further on, the train would have reached its destination 15 minutes earlier, which is equal to 1/4 hours.
Let the distance travelled before the problem occurred be z km.
Therefore, the distance travelled from the point where the problem occurred to the destination = (y - z) km.
New time taken to cover the distance (y - z) km at the new speed = (y - z)/(x/2) = 2(y - z)/x hours
The train reaches its destination 15 minutes earlier, which is equal to 1/4 hours.
Therefore, the time taken to cover the distance y km at the original speed = (2(y - z)/x) - 1/4 hours.
Equating the two expressions for the time taken to cover the distance y km at the original speed, we get:
(2y/x) + 3/4 = (2(y - z)/x) - 1/4
Simplifying, we get:
z = 30
Substituting this value in any one of the above expressions for time taken to cover the distance y km at the original speed, we get:
(2y/x) + 3/4 = (2(y - 30)/x) - 1/4
Simplifying, we get:
y = 120
Therefore, the speed of the train = x = (2y)/[(2y/x) + 3/4] = 30 km/hr.
Hence, option A is the correct answer.
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