Aptitude - Problems on Trains - Discussion

Let,
Speed of train - x
Train Passes 1st person walking in the same direction
=>Speed = (X-4.5)*8.4.

Train Passes 2nd person walking in the same direction
=> Speed= (X-5.4)*8.5.

Now,
(X-4.5)* 8.4= (X-5.4)* 8.5,
8.4X - 37.8 = 8.5X - 45.9,
45.9 -37.8 = 8.5X - 8.4X,
8.1 = 0.1X,
=>X = 8.1/0.1.
=> X = 81 Km/hr.

4.5 * 8.4 - 5.4 * 8.5 = 45.9 - 37.8 = 8.1.

It is very simple, now there is two person p1 and p2.
So, first we should find the distance for the two people.
P1 = 4.5 * 5/18 * 8.4,
P1 = 10.5 m/s.
P2 = 5.4 * 5/18 * 8.5,
P2 = 12.75 m/s.
Anyways they are in the same direction so;
Distance = (p2 - p2),
= (12.75 - 10.5),
= 2.25 m/s.
Time = 8.5 - 8.4.
Time = 0.1 sec.
Speed= distance/time * 18/5.
= 2.25/0.1 * 18/5,
= 81 km/hr.
Thank you

Let be considered x is a length, y is a speed, p1 and p2 both represent the person.

Step 1 : p1, p2 speed given for km/hr, Time is given for seconds so km/hr convert to m/s.


P1 => 4.5 * 5/18 = 1.25 m/sec and,

p2 => 5.4 * 5/18 = 1.5 m/sec.

Step 2 : Length or distance (m) = (train speed - person speed) m/sec * time.

x = (y - 1.25) * 8.4,

=> x = 8.4 y - 10.5,

=> 8.4 y - x = 10.5,

x = (y - 1.5) * 8. 5,

=> x = 8.5 y - 12.75,

=> 8. 5 y - x = 12.75.

Step 3:

8.5 y - x = 12.75

8.4 y - x = 10.5
----------------------
0.1 y = 2.25
----------------------

=> y = 22.5 m/sec.


Step 4 : m/sec convert into km/hr (ans is given for km /hr).

y = 22.5 * 5/18

= 4.5 * 18

= 81.0 km/hr.

For m/sec to km/hr conversion, we need to multiply with 18/5 only know.

Then why here it is multiplied with 5/18.

Hi, Can anyone tell me, what is the basic difference between Relative and Average speed?

(x - 1.25) x 8.4 = (x - 1.5) x 8.5.

At this stage, if I multiply both sides with 10. And try to do the solution. The result will change. Result = 117 m/sec.

Let's break it down step by step:

Step 1: Calculate the relative speed of the train concerning the first person:
Relative speed = Distance / Time = (Speed of train - Speed of first person) × (3600 s / 1000 m).
Let's denote the speed of the train as x km/h.
Relative speed = (x - 4.5) km/h × (3600 s /1000 m) = (x - 4.5) × 3.6 m/s

Step 2: Calculate the distance covered when overtaking the first person:
Distance = Relative speed × Time = (x - 4.5) × 3.6 m/s × 8.4 s = 30.24(x - 4.5) m.

Step 3: Similarly, calculate the relative speed and distance for the second person:
Relative speed = (x - 5.4) × 3.6 m/s.
Distance = (x - 5.4) × 3.6 m/s × 8.5 s = 30.6(x - 5.4) m.

Step 4: Since the distance covered is the same in both cases (the length of the train), equate the two expressions:
30.24(x - 4.5) = 30.6(x - 5.4).

Step 5: Solve for x:
x ≈ 72 km/h,
Therefore, the speed of the train is approximately 72 km/h.

Let the speed of train be x m/s, & the distance be y m; here, 4.5km/hr = 1.25m/s and 5.4km/hr=1.5m/s.

Aaccording to question, y/(x-1.25)=8.4, y=8.4x-10.5 ----(i)
Again, y/(x-1.5)=5.4, y=5.4x-8.1 ----(ii)

Solving (i) & (ii), x =22.5 Ans: 22.5 m/s.

How 2.25 came? Please tell me.