Aptitude - Time and Distance - Discussion

Can anyone please explain me this solution easily?

Let car speed = x*100%.
= x * (100/100) = x kmph. // just for understanding

Train is 50% more than car
So train speed = x*(100+50)/100 = 150x/100 = 3x/2 kmph.

In the second step. Let us consider an example a train can reach the destination without stopping at the stations in 10 mins. So the actual time is 10 mins. If it takes extra 2 mins while stopping at the stations. So 10+2=12 mins.

A car if totally takes 12 mins to reach the destination. Train Time taken by train i.e. 12 mins = Time taken by car i.e. 12 mins //Both takes equal time.

10(actual time)+2(extra time) //train = 12 //car.

12-10 = 2 ---->1

NOW COMPARING 1 with our problem. The Extra time taken for the train is given that is 12.5 mins.
Hence the equation will be:
(time taken by car) - (actual time taken by train) = extra time taken by the train.

75/x -75/(3x/2) = 12.5/60.

Since we don't know the time taken by car. Time = distance/speed. So, 75/x similarly for train as 75/(3x/2).

So 75/x -75/(3x/2) = 12.5/60. By solving get the x.

Hi, Actually we get speed as 25 only since.

Speed = Distance/(Time x Extra time).

Speed = 25/(125/600) => (25 x 24)/5 = 120.

Hi guys let me explain in this way.

Given that both reached the distance 75 km at the same time.

That indicates the time taken by car is equal to the time taken by train.

However the time taken by train also includes the delay times due to stations.

Thus,

Train time = distance/speed + 12.5 min (total time).

Cars time = distance/speed (total time).

As distance = 75 km it is clear but.

The speed of train is 50% faster, means 50% more.

If car speed = S then 50% more is.

S+(50/100)S.

Substitute the equation and you can see the answer your self.

Time taken for car - time taken for train = 5/24 hr.

This equation is derived because both start at same time and end at same time.

Let speed of car = c kmph.

So speed of train be c + (50/100)c = (3/2)c.

Time taken by car to cover 75 km distance t1 = 75/c.

Time taken by train to cover 75 km distance t2 = (75*2/3c).

But it is given train lost 12.5 m while stopping at the stations.

So,

Actual time taken by train when stopping at stations to cover 75 km = (75*2/3c) + (12.5/60).

It is given that.

Both start from point A at the same time and reach point B 75 kms away from A at the same time.

75/c = (75*2/3c) + (12.5/60).

c = 120 kmph.

Assume the car speed as 120 km/hr.
If cars speed is 120 km/hr then it reaches 75 km in 37.5 min(explained below).

Since 120 km/hr is 120 km/60 min, which is 2 km/1 min.
Therefore for 75 km it takes 37.5 min.


Train speed is 50% higher so it will be 180km/hr.
180 km/hr is 180 km/60 min, which is 3km/min.

Therefore for 75 km it takes 25 min.
It lost 12.5 min in stopping so total time taken by train is (25+12.5) = 37.5 min.

Therefore our assumption is correct. Answer is 120 km/hr.

@Neo, your method is good. I just want to know how you got that 32.5? please elaborate?

Let as take car speed as =100 than train speed is 50% faster than car so 100+50=150.

Let the speed of the car be 10km/h and so as the speed of the train is 50% more ie 50% of 10 is 5 and so the speed of the train can be assumed to be 15km/h. Based on this assumption also this problem can be solved.