Aptitude - Time and Distance - Discussion

Speed of car=Sc ; speed of train =St
Sc:St= 100:150 ( A train can travel 50% faster than a car)
= 2:3 -----> (1)
and therefore Tc:Tt= 3:2 -----> (2)

Delay given= 12.5 min = 12.5/60hrs.
Therefore time for car, Tc= 3*12.5/60 = 12.5/20 (refer (2)Tc:Tt= 3:2 )
Distance given= 75km.
We know, Speed= Distance/Time.

Therefore, the speed of the car,
Sc= 75/(12.5/20),
= 120 km/hr.

The speed of train and car = 150 : 100 = 3 : 2.
Speed = 1/time,
Time = 2 : 3.

Delay = 12.5 for train,
So, car time = train delay × 3 = 3 × 12.5 = 37.5min = 37.5/60 = 5/8h.
Finally speed = d/t =75/5/8 =120km/h.

T:C ( speed) = 3:2.
T:C ( time) = 2:3.
Time taken by car = 12.5× 3.
Speed of the car = 120 km/h.

Let time is t.
Suppose Car is going at speed x,
Train speed will be x+(x/2) = 3x/2 -------> 1
Speed of Train(dist/time) = 75/(t-12.5) ------> 2
1 =2.
3x/2 = 75/t ----->3
Speed of car = 75/t.
x = 75/t ----> 4.
substitute 4 in 3.

By solving you get;
time of car(t) = 37.5(in min)
By converting into hr.
t = 0.625 hr.
Speed of car = 75/0.625.
Ans : 120kmph

Anyone, please explain how can be the term (150/100) mean?

How 150 came? Please explain to me.

The ratio of speeds of train and car is 1.5 : 1

Therefore the ratio of time taken by them to cover the same distance is 1 : 1.5

The train lost 12.5 mins while stopping at stations. This means if the train didn't stop at stations it would reach the destination early by 12.5 mins.

That means the difference between the time taken by train and car is 12.5 mins.

Let consider x as the time taken by train.
Then as per the time taken ratio 1 : 1.5, the difference between 1.5x and x is 12.5 mins,
Then x = 25 mins,
Then 1.5 x = 37.5 mins.

Now the car traveled 75 kms in 37.5 mins,
The speed of car is 75/37.5 kms per min.
Speed of car = 75000/2250 m/s
i.e., 100/3 m/s.
Converting m/s into km/hr-
i.e., (100/3) * (18/5) = 120 kmph.

150/100 came because train is 50% faster
So, first find the 50% of 100 = that is 50.
Now add the 50 to the total 100% of car = 150.

Speed of car = Sc ; speed of train = St.
Sc : St = 100:150 ( A train can travel 50% faster than a car)
= 2:3 -----> (1)
And therefore Tc:Tt= 3:2 -----> (2)

Delay given= 12.5 min = 12.5/60hrs.
Therefore time for car, Tc= 3 * 12.5/60 = 12.5/20 (refer (2)Tc : Tt = 3:2 )
The distance given 75km.
We know, Speed= Distance/Time.

Therefore, the speed of the car,
Sc = 75/(12.5/20),
= 120 km/hr.

Train 50% faster so,
Tr:ca = 150:100(or) 3 : 2,speed
Train 12.5 min.
So ,3 * (12.5/60) = 12.5/20,time
Distance = 75
Speed = distance ÷ time.
Speed = 75 ÷ (12.5/20)
Ans : 120 km/hr.