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 1 of 24.
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)
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.
Niveditha said:
1 decade ago
Anyone please help me how this x+y is divided.
Arjun said:
1 decade ago
(27x+17y)/x+y=23 how did used that step?
Janardhan said:
1 decade ago
It's correct method to solve this problem.
Boomathi said:
1 decade ago
very good solution....
Arun said:
1 decade ago
Based on the below formula -- >
If two trains of length a(i.e. 27x) metres and b(i.e. 17y) metres are moving in opposite directions at x m/s and y m/s, then:
The time taken by the trains to cross each other (i.e.23 sec) =
(27x + 17y)
```````` secs
(x + y)
Therefore, the above solution is provided based on this derivation. Its given in the formulas section.
If two trains of length a(i.e. 27x) metres and b(i.e. 17y) metres are moving in opposite directions at x m/s and y m/s, then:
The time taken by the trains to cross each other (i.e.23 sec) =
(27x + 17y)
```````` secs
(x + y)
Therefore, the above solution is provided based on this derivation. Its given in the formulas section.
Mohit sahu said:
1 decade ago
Friends its easy to undrstnd as the qustn says that d trains r moving in oppste drtn that means the total distance travveld by the trains wen they crosses the person will be equal to the total distance travlld by dem in crossng each other.
Mathematly we can also better undrstnd ths by wrtng tht equation as
27x + 17y = 23(x + y).
Mathematly we can also better undrstnd ths by wrtng tht equation as
27x + 17y = 23(x + y).
Vivek said:
1 decade ago
How the (27x+17y)/x+y=23 formula comes?
Sunny(sunil) said:
1 decade ago
http://www.indiabix.com/aptitude/problems-on-trains/formulas
Look at this link then you can understand why we use x+y down there!
Look at this link then you can understand why we use x+y down there!
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