Aptitude - Problems on Trains - Discussion

90y - 5 = x, 90y - 9x = 100.
Putting the value of x in 2nd so 90y - 81y + 45 = 100,
So after solving, y=55/9,
The put the value in any equation then we get x=50m,
Thank you.

I didn't understand the solution, anyone explain it please.

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

Its pretty simple just follow the short trick i.e we know that,

Distance= Time*speed.
So,
Distance=9*10*2*5/18 just solve this you will get the answer in a minute i.e 50 m.

Simplify to the easy method :

Distance we don't know:
s = s.
(s-2)*9/60*60=(s-4)*10/60*60---> Equation 1.
9s-18=10 - 40.
s=22--->Equation 2

Substitute equation 2 into 1.

Ans:180
Because we convert into meter & multiply by the 5/18 then we got.
180*5/18 = 50m.

Instead of taking 2 variables.

Step1 : Simply find the velocity of the train. If velocity is known we can find the distance, since time is already;

Given.
(x - 5/9)*9 = (x - 10/9)*10,
81x - 45 = 90x - 100,
==> x = 55/9.

Step2 : Since we know the time for each man, take anyone say the man with velocity 10/9.
Relative velocity = (55 -10)/9 = 5/9.

Step3 : Distance = relative vel * time.
x = 5*10/9 = 50m.

Thank you.

Why we have not converted the speed of the train in m/s initially? Anyone explain it, please.

Good, Thanks @Anushree.

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!

Why 5/9 is subtracted with y? Please any one tell the answer.