Aptitude - Time and Distance - Discussion

@Nen.

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

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

By solving this we get the answer.

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.

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.

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.

Thanks, @Swathi.

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

How to came 9 kms and why we choose 54 kmph rather 45 kmph.

See it is covering 54km - 45km = 9km extra distance right. But that extra distance it is covering with the speed of 54kmph. So, time taken t = distance/speed = 9km/54kmph.

= (9/54) hr = (9 * 60/54) min = 10 min.

Take it as ratio type 45 (9 * 5) : 54 (9 * 6).

Then convert it (54) to 60mins 50 : 60.

So 60 - 50 = 10 that's it.

@Sundar,

Can you explain in an easy way?

Given in the question to find out the number of minutes the bus stops per every hour.

So let us consider that the bus travels for 1 hr. The distance travelled without stopping = 1 * 54 = 54 kms.

Let the bus stops for x mins in 1 hr. So the 54 kms are covered in 1 + (x/60) hrs (converting x mins to hrs).

So, 54 = 45 * (1 + (x/60) ) => x = 12. Now the total time taken = 1 hr + 12 min = 72 min.

This means that the bus stops for 12 min in every 72 mins. We have to calculate the time the bus stops in 60 mins.

So, (12 * 60) / 72 = 10 mins.