Aptitude - Time and Distance - Discussion

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.

We got that,

Eq 1: 1/x+4/y=1/15 =>1/x=1/15-4/y.
Eq 2: 1/x+2/y=1/24 =>1/x=1/24-2/y.

Now equate the 1/x values.
i.e 1/15-4/y = 1/24-2/y =>2/y = 1/15-1/24.

So you get y = 80.
By submitting y in the eq 1: 1/x+4/80=1/15 and you get x =60.
X : Y = 60:80 =>3:4.

@Karan.

It's Given in the question;
Distance by train=200.
Remaining distance by car, So 600-200 = 400 is the distance covered by a car.

Hi, from wher that 25/3 came?

How that 200 and 400 comes? Please explain me.

It takes more 20 min. It means 8hr + 20 min. Now convert into hr then it comes 20/60= 1/3. So time is 8hr+1/3hr= 25/3 hr.

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

I didn't understand the step of solving the equation 1 and 2. Please someone explain me.

Hello.


Here we can solve the equation 1 & 2 by multiplying equation 1 & 2 by number 2.

i.e. multiply eq 1 with 2 it becomes,
2/x + 8/y = 2/15,
Now multiply eq 2 with 2 we get,
2/x + 4/y = 2/24.
Now, solving eq 1 & 2.
i.e. subtract eq 2 from eq 1 we, get,
Eq 1 - Eq 2.
2/x + 8/y = 2/15.
-( 2/x + 4/y ) = -2/24.
By cancellation and sloving we get:


4/y = 2/15 - 2/24.
By taking L.C.M we, get;

4/y = (8-5)/60,
4/y = 1/20.
i.e.. y= 80 then substitute the value of y in eq1 or eq 2 u will get the value of X as 60
Then their ratio is 3:4.

200/x + 400/y = 25/3.
200 (1/x + 2/y) = 25/3.

1/x + 2/y = 25/3 * 200 (multiply 3 * 200).
1/x + 2/y = 25/600.
1/x + 2/y = 1/24.

By solving this, we get 3 : 4.