Aptitude - Problems on Trains - Discussion

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.

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

5/9 * 10 * 9 = 50.

Treat both people separately.

1st compare person A(2 kmph) and train.

Speed = dist/time.
hence time = dist/speed.
Time(for A) = 9s.
Dist = length of train
Speed = relative speed btw A and train=(S-5/9)
S = speed of the train.
9 = LOT/(S-5/9) //LOT=Length of train.

Apply same for person B.
10=LOT/(S-10/9).
solve both equations and get;
LOT= 50mtrs.

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

Let me explain if anyone wants to know how to solve the value of x,

So we got both the equations ( 1,2 ) by solving (x/ y-5/9) = 9 and (x/ y-10/9) = 10,
9y - 5 = x ->(1) , 10(9y - 10) = 9x ->(2)

By substituting equation no (1) in equation no (2), we will get,
10(9y - 10) = 9(9y - 5),
90y - 100 = 81y - 45.
9y = 55.
| y = 55/9.

Now substitute the value of (y) in equation no (1) to get the value of (x)
9(55/9) - 5 = x.
55-5 = x.
x = 50.
Thank you.

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.

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.

Speed = 2 - 4 = 2kmps.
S = 2 * 5/18 = 5/9m/s.
L = s * t
L= 5/9 * 9 * 10
L= 50.

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.