Aptitude - Problems on Trains - Discussion

Use this formulae:

L = ((T1*T2)/T2-T1) * ( S2 - S1),
= ((9*10)/10-9) * (4-2),
= 90 * 2(5/18),
= 50.4 or 50.

The speed is already given in that question itself so why do you declare that as y?

Certainly! Here’s a simplified step-by-step process to find the length of the train without getting into complex details:

Given:

• Person 1’s Speed: 2 km/h (overtakes in 9 seconds)
• Person 2’s Speed: 4 km/h (overtakes in 10 seconds)

Steps to Calculate Length of the Train:

1. Convert Speeds from km/h to m/s:
• Person 1’s Speed:
• Person 2’s Speed:

2. Calculate Relative Speed:
• Let be the speed of the train in m/s.
• Relative speed with respect to Person 1:
• Relative speed with respect to Person 2:

3. Use the Length Formula:
• Length of the train when overtaking Person 1 (in 9 seconds):
• Length of the train when overtaking Person 2 (in 10 seconds):

4. Set the Two Lengths Equal:
Since both expressions equal the length of the train:
5. Solve for
• Expand and rearrange the equation:

6. Calculate the Length of the Train:
Substitute back into either length formula. Using the first person:

Final Result:

The length of the train is approximately 50 meters.

Summary of Steps:
1. Convert speeds to m/s.
2. Set up equations for lengths based on relative speed.
3. Set the equations equal to find the speed of the train.
4. Substitute back to find the length.

This streamlined process makes it easier to follow and calculate the length of the train. Let me know if you need any more simplifications!

Can solve this way: Same direction a person walk so the subtraction of speed i.e 4-2 = 2kmph.
And (2*5/18)m/s =5/9.
Now the time is 9 and 10-sec addition of two is 90.
So, 90 * 5/9 = 50.

Why we multiply 9 and 10 here? can anyone explain?

How? please anyone explain me.

Good, Thanks @Anushree.

Distance = length of the train.
D = S * T.
D = (4-2)*5/18*90,
Therefore D = 50.

S = D/T
S-2 = D/9
9(S-2) = D ------> (1)
S-4 = D/10
10(S-4) = D ------> (2)

Distances are equal as the same cross both, equating 1,2.
10S - 40 = 9S - 18.
1S = 22(Speed of train).

Taking any one person's reference;
22-2 = D/9.
20 * 9 = D,
D = 180 * 5/18,
D = 50mtrs.

Hello everyone. Please have a look at my method of solution. It is giving a different answer.

Let,

the Speed of the train = x.
Then,

With respect to the first person;
The relative speed of the train = (x-2)*5/18 m/s.
Time is taken to cross the first person = 9s,
Length of the train = Speed * Time = (x-2)*(5/18)*9.

With respect to the second person;
The relative speed of the train = (x-4)*5/18 m/s.
Time is taken to cross the first person = 10s.
Length of the train = Speed * Time = (x-4)*(5/18)*10.

As both lengths are of the same body (train), so;
(x-2)*(5/18)*9 = (x-4)*(5/18)*10.
(x-2)*(5/2) = (x-4)*(25/9).

Upon solving, we get:
x = 22m.