Aptitude - Problems on Trains - Discussion

I do not understand this. Please explain to me.

I have a small doubt regarding the formula.

In the question, they have said to find the ratio of speed. Not the ratio of time.

So aren't we supposed to modify the formula accordingly? Please someone explain.

Why is the length of the platform not taken into consideration? Anyone, please explain to me.

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.

Given data:
t1=27 sec t2=17 sec
S=d/t,d=s * t.

d is consider as l,

l1=s1 * t1 =17 s1,l2 = s2* t2 =27 s2.

In question ,it clearly move in a opposite direction,so we have to use this formula->(l1+l2) /s1+s2.

Total time = (17s1+27s2)/s1 + s2,
23(s1+s2)= 17s1+27s2.

Rearrange it,
23s1-17s1=27s2-23s2,
6s1 = 4s2,
s1/s2 = 6/4=3/2.

So,the answer is 3:2

Very well done. Thanks.

Isn't it like X/Y = 4/6?

How come in the above solution like X/Y 6/4=3:2.
X=4 and Y=6 isn't it?

Can the ratio be 2:3? Anyone explain me, please.

Short method is;

x person 27.
y person 17 add both distances and divide the total distance and multiple the same for both persons.

27+17/23 *2.
37/23 = 1.6 *2.
1.6*2.
Ans : 3.2.

@Poornima.

Thank you for the explanation.