Aptitude - Time and Distance - Discussion

I did not understand. Please help me to get it.

The speed of the car is x km/h.
The speed of the train = x + 50x/100,
= 150x/100,
= 3x/2 km/h.

The time taken by the car = 75/x.
The time taken by the train = 75/(3x/2).

The difference between them is 12.5 minutes.
75/x - 75/(3x/2) = 12.5 minutes.

To convert minutes to hours, divide the number by 60,
Therefore,
75/x - 75/(3x/2) = 12.5/60 hr,
75/x - 75/(3x/2) = 125/(10*60) hr,
75/x - 50/x = 5/24,
25/x = 5/24,
5x = 25*24.
x = 120 km/hr.

Let the speed of car be x.
now, the train is 50% faster than a car,
i.e. speed of the train = x + (50/100)x.
= 150x/100.

Convert km/h to m/s.

S(c) = 75000/T -->(1)
S(tr) = 75000/(T-12.5x60)-->(2)
S(tr) = 3/2S(c) -->(3)

Sub (3) in (2).
3/2s(c) = 75000/(T-12.5x60).

sub (1) in above;

(3/2).(75000/T) = 75000/(T-12.5x60).
T = 3x12.5x60 ---->(4)

Sub (4 in (1) [to get the speed of the car].
S(c) = (75000/3x12.5x60 ).(18/5).
s(c) = 120km/h.

Most of people saying 1/2 instead of 3/2 is wrong.

The train is 50% more means 1/2 and also 1 for the car speed is added, So it's 3/2.

Let the speed of the train be x.

So, train speed 50% faster than car means x + x/2 = 3x/2, speed = 75km/hr,
Time delayed = 12.5 mins = 12.5/60 sec.
Now;
D/s = T; (here speed = speed of the car -speed of the train),
So,
75/x -75/3x/2 = 12.5/60.
75/x - 50/x = 5/24.
x = 25 x 24/5.
x = 120 km/hr.

Here, How can we say given time in the question is equal to the value obtained after subtraction? Please explain me.

@ALL.

Time, distance, and speed problems always assume one variable as constant and calculate the others.
See in this question, started at A and reached at B (75 km).

Both the car and the train reached point B at the same time, even though their speeds are not the same, because the train had waited 12.5 mins in between. So the train has travelled 12.5 minutes less than the total time taken by car.
So, the difference in their times is just 12.5 mins.
t1 - t2 = 12.5 mins (t=d/s)
d1/s1 - d2/s2 = 12.5 mins. ( let x is speed of the car, and 50% more will be 1.5x )
75/x - 75/(1.5x) = 12.5/60 hr.

Solve this as it has only 1 unknown, we will get the speed of the car.

Thanks for explaining the answer @VIJETH BK.

I didn't understand this, anyone please explain to me?