Aptitude - Time and Distance - Discussion

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.

I don't understand. Please explain me in detail.

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.

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.

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.

Thanks for explaining the answer @VIJETH BK.

(The train can travel 50% faster than a car).

This means the train is travelling 1/2 time faster than the car, not 3/2 time faster.

Final Answer: Speed of the car = 100 kmph.

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