Aptitude - Time and Distance - Discussion

Distance =600 km
Time take =8 hrs.
Distance =Speed *time Then
Time = Distance/Speed
SO
Total time = Total Speed.
Suppose train speed = X, And Car speed = Y.

Then 120/X +480/Y = 8 hrs.
Then 120 take common,
120[1/X+4/Y] =8 hrs.
1/X+4/Y = 8/120
1/X+4/Y = 1/15 ----> (1) equation.

Total time is 8 hrs.20 min. mean(8*1/3)
8*1/3 =25/3
200/X+400/Y =25/3 Then
200 Common.

200[1/X+2/Y] = 25/3.
1/X+2/Y =25/3*200.
1/X+2/Y =1/24 ---> (2) equation.

Solve both (1),(2) eqn.

We get 2/Y =1/15-1/24,
When solve this we get 2/Y =1/40,
Y=80 put this value on the first eqn.
You get X = 60
So the ratio of X:Y 3:4.

How to find the x and y values can anyone help me?

Very good explanation, Thanks @Kavitha.

Thanks @Rahul Singh.

@D.Rajkumar.

Actually when we say 8.2, the 0.2 there is out of 1 unit or 2 out of 10 or 2 out of 100. There are however 60 minutes in 1 hour which means the same concept cannot be applied since we are calculating out of 60 and not 100. 25/3 is absolutely correct.

If the ratio is known 3:4. How can we find the speed?

Thanks @Rahul Singh.

The second one takes 20 minute more then time is 8:20 but 25/3 is 8.3.

So, 33/4 is 8.2 is correct

Thanks @Ophi.

Train covers 80Km more and car covers 80Km less, as a result 20min more is required. Suppose train covers 240Km(i.e. 3*80) more and car covers 240km(i.e. 3*80) less than it tooks 60min(i.e. 3*20) more.

Similarly, if train covers 480km more and car covers 480km less than time will increase by 120min i.e. 2hr. It means it the whole journey is covered by train only than it takes 10 hrs(8+2) to complete it. so speed of train = 600/10 = 60km/hr.

Now, time taken by train = 120/60 = 2 hrs.
So, time taken by car = 8 - 2 = 6 hrs.
And, speed of car = 480/6 = 80km/hr.
Speed of train : speed of car = 60:80 = 3:4.