Aptitude - Time and Distance - Discussion

It's easy to solve when we go by options.
In question, they have given details about the second train. Now using formula s=d/t ,we get s=400/4=100.

First train speed is not known, but the ratio of speeds is given in question as 7:8.
We got second trains speed i.e 100,

Now let's look into the options (the options tell about first trains speed ) and when we take the last option 87.5:100 (//speed of first train: speed of the second train ) we get 7:8.Thus concluded that the last option is right.:)

We can calculate this by a simple method.

Here the distance = 400 km.

And the time taken to cover this distance by the second train is 4 h.

Therefore the speed of the second train will be 400/4 = 100 kmph.

The ratio of the speed of both the trains is 7:8.

Therefore the speed of 1st train will be 100*7/8.

= 700/8.

= 87.5.

So the speed of the 1st train is 87.5 kmph.

We know that speed = distance/time.

So, consider speed of 1st train is s1 similarly s2.
Given ratio of their speeds is s1:s2 = 7:8.

Therefore, s1/s2 = (d1/t1) * (t2/d2) -------> (1).

Assume d1 as x, as it covers x km in 1 hour.

Therefore substituting these values in equation (1) we get,
7/8 = (x/1hour) * (4hour/400km).

By cross multiplication we get 87.5km/hr.

I don't know why they have provided a confusing method.

Here is a simple method we use the principle of ratios and direct proportion.

7/8 = x/(400/4) (Speeds are directly proportional to their ratio i.e 5.

Speed of x/Speed of y = Ratio of (speed of x/speed of y).

Hence 7/8 = 4x/400 -> x = (400*7)/(8*4) = 878.5 simple as that.

Let Distance is 2D=D for the first halt+D for the second half.

Total time =10hr.
Time taken in first half+Time taken in second half=10hr so,
T1/2 + T/2=10 Now Time = distance/speed.
D/21 + D/24=10.
(D*24 + D*21)/21*24=10 solve it we get.
45x=5040 = D= 112 it is the time taken half journey.
2D=112*2=224km.

I HOPE YOU UNDERSTAND.

Easy way is here.

We know that ratio of two train is = 7:8.

Speed of 1st train = ?

Speed of 2nd train = 400\4 = 100 kmphr.

So, 1st train:2nd train = 7:8.

? : 100.

So divide 100 by 8 we will get = 12.5.

Now multiply 1st train ratio with 12.5.

i.e 12.5*7 = 87.5.

So the speed of first train = 87.5 kmphr.

Its a ration sum..
then..
Second train runs at 400kms in 4 hours, so in 1 hour its speed is 400/4=100kms/hr.

Now according to ratio concept:-

7:8
means..
total is 15..
then 8/15*x=100
we get,187.5 total speed of both the tain.
now
for first train speed..
7/15*187.5= 87.5 km/hr

Let the second train covers 400 in 4 hrs.
So, per hour it covers 100 km.

so, we have a ratio of 7:8.
if we consider 100 km in units each 10 km will be 1 unit.
But we have only 8 units so here 1 unit is equal to 12.5 km.

12.5 x 8 = 100.0.
then, 12.5 x 7 = 87.5 kms.

Speed of the 2nd train =
Total distance it traveled / total time taken
= 400 / 4 = 100kmph
Therefore,
according to the ratio provided,
8x = 100 kmph
x = 12.5 kmph
therefore the the speed of the second train =
7x = 7 (12.5) = 87.5 kmph
I hpoe that is easy.

The odometer of a car reads 57321.0 km when the clock shows time 8.30am. What is the distance moved by a car at 8.50 am, the odometer reading has changed to 57336.0km. Calculate the speed of the car and express the speed in km/hr.

Solve and find the solution.