Aptitude - Problems on Trains - Discussion
Discussion Forum : Problems on Trains - General Questions (Q.No. 4)
4.
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
Answer: Option
Explanation:
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.
 |
27x + 17y | = 23 |
| x+ y |
27x + 17y = 23x + 23y
4x = 6y
| |
x | = | 3 | . |
| y | 2 |
Discussion:
233 comments Page 24 of 24.
Niveditha said:
1 decade ago
Anyone please help me how this x+y is divided.
K.kiran kumar said:
1 decade ago
I can't get this step
(27x+17y) / (x+y) = 23
Why we have to use this? can any one explain me.
(27x+17y) / (x+y) = 23
Why we have to use this? can any one explain me.
Poornima said:
2 decades ago
Let me explain in detail if anyone still not understood yet.
Please remember the formula for finding speed. Speed = Distance/Time.
Therefore, Distance = Speed x Time.
If a train crosses a man/pole/post/tree in T seconds, and speed of the train is S m/s, then
Then, the Length of the Train = (Speed x Time) = ST metres.
Note: Here, the distance traveled by train in T seconds at the Speed of S m/s is equal to the length of the train.
Now, lets come to the given problem.
Let speed of the first train = X.
Time taken taken by the first train to cross a man = 27 seconds.
Therefore, Length of the first train = Speed x Time = X x 27 = 27X metres.
Let speed of the second train = Y.
Time taken taken by the second train to cross a man = 17 seconds.
Therefore, Length of the second train = 17Y metres.
Important Formula:
If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then:
The time taken by the trains to cross each other = (a + b) / (u + v) sec.
Given that, (a + b) / (u + v) = 23 seconds.
Here, a = 27X, b = 17Y and u = X, v = Y.
Therefore, (27X + 17Y)/(X + Y) = 23.
=> 27X + 17Y = 23X + 23Y
=> 4X = 6Y
=> X/Y = 6/4 = 3/2
=> X : Y = 3 : 2.
Please remember the formula for finding speed. Speed = Distance/Time.
Therefore, Distance = Speed x Time.
If a train crosses a man/pole/post/tree in T seconds, and speed of the train is S m/s, then
Then, the Length of the Train = (Speed x Time) = ST metres.
Note: Here, the distance traveled by train in T seconds at the Speed of S m/s is equal to the length of the train.
Now, lets come to the given problem.
Let speed of the first train = X.
Time taken taken by the first train to cross a man = 27 seconds.
Therefore, Length of the first train = Speed x Time = X x 27 = 27X metres.
Let speed of the second train = Y.
Time taken taken by the second train to cross a man = 17 seconds.
Therefore, Length of the second train = 17Y metres.
Important Formula:
If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then:
The time taken by the trains to cross each other = (a + b) / (u + v) sec.
Given that, (a + b) / (u + v) = 23 seconds.
Here, a = 27X, b = 17Y and u = X, v = Y.
Therefore, (27X + 17Y)/(X + Y) = 23.
=> 27X + 17Y = 23X + 23Y
=> 4X = 6Y
=> X/Y = 6/4 = 3/2
=> X : Y = 3 : 2.
(6)
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