Aptitude - Time and Distance - Discussion

Just read the question carefully.

Both car and train starting and finishing at a same time that means they are taking the same time to reach A to B.

now we know that,
time=distance/speed

distance= 75
speed of car = x
speed of train = speed of car + 50% of speed of car = x+[50/100]x or 3x/2

now
travelling time of car = time taken in travelling +no waiting
75/x + no waiting
time of train = time taken in the travelling + waiting
= 75/[3x/2] + 12.5/60 hr

and both times are equal as in question it is given they are starting and reaching at the same time let we compare them.

75/x =75/[3x/2] + 12.5/60
which will give x= 50.

Let me clear this.

We can assume the speed of car as X
Now the speed of train (as per question) = X+X/2 = 3X/2
Distance (as per question) = 75 km
So time = distance/speed
For car its= 75/x
For train = 75/3x/2 now multiply 2 to 75 = 150/3x = 50/x
Now we have to add waist time to the train speed = 50/x+ 12.5/60
12.5/60 because time is given in minutes and we need it in hour so multiply 12.5 with 1/60 So it's = 12.5/60 or we can write it like 125/600= 5/24

Now the new speed of the train is 50/x+ 5/24.

put car speed = trains speed

75/x = 50/x+5/24.
or
75/x -50/x =5/24.
or
75 - 50
--------- = 5/24.
x
or
25/x = 5/24.
cross multiply.

24*25 = 5x.
600 = 5x.
x= 120 kmph.

Many have asked how 3/2x came?

According to me "train travels 50% faster than car"
Let the speed of car be x.
Then the speed of train is,
The speed of car+ 50%speed of car (as per question)
ie,
x+ 1/2x.
=3/2x.

Train and car covers the same distance in same time. But train 50%faster than the car.

The Train stops at stations 12.5.
It means they cover 75km in 25minutes.
So convert minutes into hr (75÷60=12/5).
So that the speed of the train = 75*12÷5=180,
50% of 120 is 60,
180 - 60 = 120.
So Speed of car is 120km/hr.
Because train is faster than car 50% is given above.

***Assume the speed of car be 'a'.

TIME OF THE CAR = distance of car/speed of car.
= 75/a.


Since train is 50% faster than car, therefore
50% of a=====50/100 X a===1/2 X a====a/2 (this is 50% of the car speed),
a + a/2====3a/2 (train is 50% faster than car).

TIME OF THE TRAIN = distance of train/speed of train.
= 75/(3a/2),
= 150/3a,
= 50/3a.

Time of the car - time of the train = 12.5 min ----------------------> MAIN FORMULA.

75/a - 150/3a = 12.5/60 (since we are calculating in km/hr, so divide it by 60),
75/a - 50/a = 12.5/60,
= 120.

Good explanation, thank you @Rihan.

Let, Speed of the train be X kmph.

Than, Speed of the train= x + (x * 50/100).
= x + x/2,
= (2x+x) / 2,
= 3x/2.

Let speed ratio=car:train=100:150=2:3.

Here distance is same so as per the rule "if distance is same then speed ratio is inversely proportional to time"

Speed ratio = 2:3
Time ratio = 3:2

Therefore car usual time = 3 * 12.5 = 37.5 min.
And train usual time = 2 * 12.5 = 25 min.

Now, speed of car = Distance/time,
= 75kmph / 37.5 min,
= 2.
Now convert into hour=2 * 60 = 120kmphr.

Good explanation, thanks @Raihan.

Hi, can you please explain why we are subtracting the time of car and train to get 12.5 minutes?