Aptitude - Time and Distance - Discussion

Can any one please tell me how that 125/(10x60) came?

Another shortcut yet simple method I would like to share wherein forget the hassle of x and y so the method is as follow:

Time taken by the car and train to reach the destination is the same and if you read the question carefully it is mentioned that the train has halted for 12.5 minutes at the stations that means just because of 12.5 minutes halt the train and the car covered 75 kilometers at the same time.

Just because of 12.5 minutes the train misses to cover 50% of the route that means the total time taken by the train and the car to reach the destination is 37.5 minutes ( working- 75km/2 =37.5, so in 12.5 minutes stop it missed 37.5km, hence the train took total 25 mins to reach the destination + 12.5 mins halt = 37.5 mins. )

Now comes the cross multiplication part. 37.5 mins = 75 kms
60 mins = ? (working- we already know how much kilometers it can cover in minutes but we want to find km/hour, so 1 hour = 60 mins.)
= (60*75)/37.5
=120.

To solve in this way you require a bit logic and good knowledge of cross multiplication. Still if you don't understand this method I suggest you to go for the Admins method.

75km/s * 60 second = 4500sec,
50%-12.5 the train lost =37.5,

Speed = Distance/time.

then 4500sec/37.5 = 120km.

Let, car speed = X km/min.

Train speed = X + x* (50/100) Km/min.

=X+X/2 km/min.

=3X/2 km/min.

Time of car t =75/X.

Time of Train t =75/ (3X/2).

According to the question.

75/X=75/ (3X/2) +12. 5.

>> 75/X-150/3X=12. 5.

>> (225-150) /3X=12. 5.

>> 75 = 37. 5X.

>> X = 2 Km/min.

So car speed 1 minute to 2 km.

Car Speed 60 minutes to (60*2) = 120 km/h.

Why to subtract the speed of the train from speed of car (75/x-75x/[3/2])?

Can anyone help me by explaining?

Late Train speed = X km/hrs.
Than Car speed will be = X+X/2 =3X/2 km/hrs,
Time_train - Time_car = Time - train stop.
75/X - 75/(3/2)X = 12.5/60,
75/X - 50/X = 25/120,
25/X = 25/120.
X = 120 km/hrs Ans.

Let the car speed be x.

Speed of train = 150/100x = 3/2xkmph(explain 25*3/25*2).
75/x-75/3/2x = 12.5/60.
75/x-75/3/2x = 125/600.
75/x-75*2/3x = 5/24.
75/x-150/3x = 5/24.
75/x-50/x = 5/24.
25/x = 5/24.
x = 25*24/5.
x = 5*24.
x = 120.

@Yogi,

Train increase speed 1/2, means time decrease 1/3,
This 1/3 =12.5 minute. = 12.5/60 = 5/24 hour,
Speed = distance/time.
Speed(train)= 75km/5/24 = 360km/h,
Car speed = train speed/2,
Car speed =120kmph.

The Speed of train increase by 1/2, means time reduce by 1/3, this 1/3 time reduction is 12.5 minute.

So, 1/3 = 12.5/37.5.

Means the car will take three-time of 12.5 minutes which 37.5 minutes.
75 x 60/37.5 = 120kmph.

It's given that both Car and the train covers 75kms at the same time (t1=t2)
t=d/s

Let's assume car speed as 'x' km/hr.
Train Speed = x + x/2.
=3/2x.

t1=75/x.
t2=75/(3/2)*x.

t1 = t2+12.5mins extra time.
Then solve by converting 12.5 mins to hr by dividing by 60.