Aptitude - Time and Distance - Discussion

Both reach same time but suppose TI but train losses 12.5 so train time is TI-12.5 and car time is TI.

Now WKT time=distance/speed, x be the speed of car and 3x/2 speed of the train, both distance is same.

Substitue in formula for train time=TI-12.5 dis=75 speed 3x/2 we get (TI-12.5)=75/3x/2
for car time=TI speed=x dis=75 we get TI=75/x now substitue TI In above trian equation we get;

75/x-12.5 = 75 * 2/3x convert time into 12.5/60 and the result:120km/hr

Here we take 150/100 because it is given 50% more and always we have to take 100 as a base value here it is 50%more so 100+50/100 = 150/100 = 3/2.

(If it is given less than 50% then 100-50/100 = 50/100 = 1/2.

I hope you all understand.

Can anybody tell me why we need to subtract 75/x with 75÷3/2x instead we can add it also right?

The speed of car : speed of train :100:150=2:3.
The time needed for the car: time needed for train =3:2.
i.e., the train only takes 23 of the time taken by car.

Since both the car and train start and reach at the same time,
13 of the time needed by car is 12.5 minutes.
Time needed by the car =3*12.5 min.

Therefore, speed of the car =75(3 * 12.560)=120 km/hr.

Anyone explain me from 2nd step.

Let the speed of car be x.

Since the speed of the train is 50% more than the speed of the car, speed of train will be x+(50% of x).

i.e x+x/2 which is 3x/2.

now, let t be the time taken by car. therefore t=75/x --->eq(1)

(using time= distance/speed).
given that train loses 12.5 mins. therefore the total time travelled by train is t-12.5 min (note that both train and car took the same time to reach B. that's why we can take t as the time taken by both car and train)

using time=distance/speed formula, we will get;

t-12.5=75/(3/2x).
which can be rewritten as t-12.5=75/1.5x ----> eq 2
from eq1, we have x=75/t , sub in eq 2.

t-12.5=75/1.5x.
t-12.5=(75*t)/(1.5*75),
t-12.5=t/1.5,
solving which we get.
t=37.5 min=37.5/60 hrs.

as we have x=75/t (from eq1).
x=(75*60)/37.5,
x=120km/hr.

The speed of the train is 50% more than a car.
If the car travels at x kmph then 50%of x is x/2kmph.
Note train travels 50% more which means actual x and 50% of x is x/2 together (x+x/2) =3x/2.

Actually he gave 50% more not 50% times.
so, the speed of train = speed of car + 50% speed of car.
= x+(50/100)*x = 3/2x.

Given that, time of car - time of train = 12.5 min,
(75/x) - (75/(3/2*x)) =125/10 min,
75/x(1 - (2/3)) =125/(10*60) hrs,
1 = 125x/600,
x = 120 kmph.

I think there should be 50/100 not 15/100 right?

Here why we used 75/x-75/(3/2)x=125/10*60.
Please anyone can explain me?.