Aptitude - Time and Distance - Discussion

Thanks, @Swathi.

By using formula, we can solve these in less time.

Simple formula:

Stoppage time = (se - si) / se.
Where se = excluding stoppage.

si = including stoppages.

st = (54 - 45) / 54.

= 9/54.
= 1/6 hr.
= 1/6 * 60min.
= 10min.

It's simple.

Take it in this manner.

In 1 hour without a stoppage, it travels 54km and with stoppages it travels 45km. So by subtracting we get 9km as the distance that could've travelled more.

Time = dis/speed = 9 * 60 (for mins) /54 = 10 mins.

I don't know whether my answer would satisfy but here are they to help, (though lenghty).

Somewhere asking why one hour is considered or 54kmph - 45kmph = 9kmph speed how it is 9km?

Ans: Read question completely it asks within one hour. So we get it by calculating for one hour.
(this is same reason why answer is not 12 if you consider 45 you will get 12 but it is wrong)

Second question is why 54 and not 45 its because 9km was not travelled in 45 its included (I'm not referring to stops included) in 54 so what's the time taken for that so we calculate the time for that extra 9km travelled that was done with 54 and not with 45.

Now distances with speed 54kmph and 45kmph within one hour (mentioned in the question) is 54km and 45km respectively. Now it could have travelled 9km additional if stops excluded (54km - 45km).

(calculating time taken to travel is same as calculating time spent for stoppages).

As its asking in one hour and answer are in minutes (mentioned in the question) we use 60minutes.

For 1km it takes {60min/54km = 1.11minutes per km. Now for 9km it takes 9km * 1 11111min/km = 10minutes}.

This is why people wrote : time= ( (60/54) * 9) =10.

Answer 12 is not correct.

@Nen.

60 mins(1hr) ------> 54kms,
? mins -------------> 9kms.

1 * 9/54 = 1/6 = 10mins.

By solving this we get the answer.

Hi, I'm not getting this. Can anyone explain me clearly?

Why we considered 54?

Let's do this way:
Let us consider a distance d km and the second vehicle takes x time more.

Then,
D = 54km/hr * 1hr as 54km/hr is without stoppage so it'll take.

Less time.
D = 45km/hr * (1 + x) including stoppage will take more time to.

To cover d km.

54 * 1 = 45 (1 + x).
54 - 45 = 45x.
9 = 45x.
The, x = 9/45 = 0.2hr.

=> 0.2hr = 0.2 * 60 min = 12 min.

Well said @Nitesh Nandwana.

It's simple and easy to solve.

Formula:

If a body moves at an average speed of V1 km/hr to cover a distance of D km without stopping and moves at an average speed V2 km/hr to cover the same distance.

Then stoppage time/hour is: (V1-V2) /V1.

= (54-45)/54 = 10 mins.

We are taking 9/54, because car is moving @ 54 not 45 km/hr. The question is on average speed which means total distance divided by total time.

Now, because car waits for some minutes at stops that is why average speed gets decreased. So, speed is same which is 54 km/hr, but including stoppages total time has increased. Therefore average speed comes down.