Aptitude - Time and Distance - Discussion

5. 

Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

[A]. 9
[B]. 10
[C]. 12
[D]. 20

Answer: Option B

Explanation:

Due to stoppages, it covers 9 km less.

Time taken to cover 9 km = 9 x 60 min = 10 min.
54


Kanmani said: (Aug 17, 2010)  
How to get 9 km?

Sundar said: (Aug 17, 2010)  
It is obtained by 54 kmph - 45 kmph = 9 kmph.

Girishkumar said: (Aug 18, 2010)  
How did 9/54 come?

Shaju said: (Sep 11, 2010)  
Hey its 54 kmph and 45 kmph. Can you explain how you got 9 km by subtracting the speeds of bus at different circumstances?

Nitesh85 said: (Oct 9, 2010)  
@Mr.Shaju

54 - 45 = 9 km is absolutely correct because we are calculating relative results.

Nitesh Nandwana said: (Oct 9, 2010)  
@Girishkumar hi itz simple.

Because 54km in 1 hour.

So 1 km in 1/54 hour.

So 9 km in 9* (1/54) *60 min (1 hour = 60 min).

Sam said: (Oct 19, 2010)  
Why to consider 54 rather than 45?

Ranjit said: (Nov 13, 2010)  
First we have to see what they asked. For how many minutes does the bus stop per hour. For that we have to consider the value 54 (exclude stoppages) ie. , if we consider the value 45 the bus has been already stopped so we are considering value 54.

Jaya said: (Nov 23, 2010)  
The easy method: For 1 hour the bus travels for 54 km then for one min its 54/60=0.9km.

So if the bus stops for one minute it travel 0.9 km less so if the bus travels 9 km less then it might stopped for 10 min.

Krishna said: (Dec 17, 2010)  
Excellent explanation thank you JAYA. Thanks a lot.

Ravindhar Reddy said: (Dec 17, 2010)  
great explanation .
thank you jaya.

Ankit said: (Dec 23, 2010)  
Great jaya. !

Sumit said: (Feb 8, 2011)  
Jaya your are great.

Kushal said: (Feb 13, 2011)  
60 mins(1hr)--------------->54kms
???mins--------------------->9kms
solving we get the ans:-)

Sheela M B said: (Mar 29, 2011)  
Well thought by Jaya ans Kushal. Gr8 guys!!

Simanta Chatterjee said: (Apr 25, 2011)  
Awesome kushal. Hats off.

Hari said: (May 24, 2011)  
Excellent kushal. This method is easy.

Reeta said: (Jun 6, 2011)  
Great jaya.

Rahul said: (Jun 27, 2011)  
How did u get as 9 km, as they have subtracted the two speeds...!!!! if they have subtracted them it would result as 9 km/hr!!!! Then hw s it possible to get the time...???? May be the question is wrong..!!!!

Nivi said: (Jul 7, 2011)  
How 9/54 came. Please explain.

Rn Pandian said: (Jul 12, 2011)  
Excellent Kushal. Hats off........

Rukshana said: (Jul 22, 2011)  
Rahul....Question is right only...Actually without stoppages it cover 54 but with stoppages it cover only 45...so only we need to subtract...to get the speed without stoppages..so 54-45=9..Then we having speed with stoppages ..so only considering 9\54 then we need to get min so mul by 60..now got?

Swetha said: (Aug 10, 2011)  
I have the same doubt that what rahul having..if we subtracting two speeds ,then we will get difference in speed na? how we got the distance 9 km?

Anoo said: (Aug 10, 2011)  
54 kms in 1 hour..but in 1 hour it travelled only 45 kms..9 kms less..
1 hour-54 kms
??? - 9kms

1x9/54 = 1/6 hour = 10 minutes

Supreeth said: (Aug 29, 2011)  
Can't we solve this question like this? if no why?

We now that, Displacement(S) = Velocity(V) * Time taken(t).
ie,s=vt.
consider 1st condition..

Let the distance travelled by bus be 'x'm.
therefore,x=54t.(without stoppage).......(1)

From 2nd condition..
x=45(t+y)........(2)
(y=total stoppage time)

Dividing 1 & 2 n solving we get bus stops for 12 mins in 1 hour.

Piyus said: (Aug 29, 2011)  
Why it will be 10 minutes instead of 12 minutes ?

Sumit said: (Oct 10, 2011)  
The time taken by the bus for i k.m is 60/54=1.11 min
so if the bus travels 9 k.m less due to stoppage
then the ans will be =1.11*9=10 min.

Chetna said: (Nov 1, 2011)  
Why we consider only 54 but not 45?

Dhruv said: (Nov 8, 2011)  
Good explanation jaya.

Ajit said: (Nov 12, 2011)  
Simple is that you hav to calculate the wasted time=time taken by bus to cover 9kms).

In one min it covers 0.9 kms.

For 9kms-?min.

You get 10min.

Kasi said: (Jan 4, 2012)  
Good explanation kushal :)

Krishn said: (Jan 21, 2012)  
I still didn't understand.

If 54km - 45 km = 9 km. That is speed reduces by 9 km/hr.

So 60/9 = 20/3 per min...now how do i proceed next?

Shro said: (Feb 18, 2012)  
Hey somebody explain it clearly 54km/hr-45km/hr=9km/hr
Why to consider only 9km?
why not 9km/hr?

The answer is clearly 9km /hr.
Then why to convert it into minutes?
it should be only 9/54= 1/6 or say 0.16

Denis said: (Mar 5, 2012)  
Thanks Kushal.

Kunal said: (Mar 30, 2012)  
If the bus doesn't stop for an hour it travels 54 km at a constant speed of 54kph. But it stops for some time 't' and covers 45 km in the remaining (60-t) mins at 54kph.

45 = (60-t) * (54/60) => t=10mins.

Afsar said: (Apr 3, 2012)  
How it take 9km. ?
It is because there is no time limit given so.
We take reference time 1hr. And each having same time.
So distance=speed*time.

Harshita said: (Apr 17, 2012)  
Hi. Please tell what is wrong in the following approach? because I'm not getting the right answer by this.

54 km/hr means in 1hr it will cover 54km.
Now if it stops of x hr the the new speed.
45=54/ (1+x).
So x=9/45 hr= (9/45) 60 min. =12 min?

Pratik said: (Apr 22, 2012)  
Let us suppose 10 min is the ans..
Let the distance covered be 54km.
Time 1 hr without stoppage.
Then 54/1 = 54 kph..
With stoppage of 10 min= 1/6 hr= 0.1667 hr
54/(1+0.1667)= 46.28 kph
---------------------------------
Let 12 min be the ans
With stoppage 0f 12 min=1/5hr=0.2hr
54/(1+0.2)= 45 kph.

Chinmayee said: (May 3, 2012)  
Why we take 54 instead of 45 ? please solve my question.

Suresh Khichee said: (Jun 20, 2012)  
D = S*T.
D = 54/1 * T ....(1) T is time taken by bus without stoppages.
D = 45/1 *( T + S ) ...(2) where S is time taken by stoppages.
By (1)& (2)

54*T = 45*T + 45*S
54*T - 45*T = 45*S
9*T = 45*S or 9/T = 45/S so ratio of T/S = 45/9

T/S = 5/1 {T=time ,S= time of stoppage }

T:S ::5:1 shows that

In 6 minute(5+1) bus takes 1 minutes for stoppage.
So In 60 minutes bus will take 10 minutes stoppage.

Murali said: (Jan 19, 2013)  
Excluding stoppages= (difference of speeds/excluding Stoppage) *60mins.

= (54-45/54) *60mins.

= (9/54) *60mins.

= (1/6) *60mins.

=10mins.

Akriti said: (Mar 21, 2013)  
Here speed is given - 54 (excluding stoppages), 45(including ).

Time taken at stoppages -d/t.

So 9 kmph, distance - 9*60.

540/54 because (distance /time), we got 10min.

Mukesh Kumar Jena said: (Aug 11, 2013)  
Let for a hrs, bus runs at 54 kmph.

And b hrs, bus runs at 0 kmph.

So avg speed => 45=(54*a)/(a+b).
=> a=5b.

Since we need for 1 hour;
a+b=1 hr.

We got ; b=1/6 hr stoppage time = 10 mins.

Kaushal said: (Aug 18, 2013)  
Why it use 54 km/hr with 9 km not use the 45 km/hr?

Bipana said: (Aug 22, 2013)  
1hr----- 54 km without stoppage.

1hr----- 45 km with stoppage.

Speed = 54 km/hr.

Bus losses (54-45=) 9 km in 1hr.

Time = distance/speed.

= 9 km/54 km/hr.

= 9*60/54.

= 10 min.

Bus needs 10 min. To travel 9 km. So it losses 10 min to travel 9 km per hour.

Chandini said: (Sep 2, 2013)  
Why should we use 54 rather than 45?

Arun KR said: (Sep 3, 2013)  
@Chandini.

Because:

Actual speed of the bus is 54 km(in 1 hour), So Due to the stops it will reduce As 45. To calculate 1 min bus traveled distance using only the actual speed (54). If We take 45 means the bus already stopped.

Aarman said: (Sep 3, 2013)  
Because @Chandini bus is going on 54 km without stopped and 45 is this stopped time the bus that why here when the bus stopped then bus is loss a time.

Poorni said: (Nov 10, 2013)  
0.9 km per minute, what it implies about? lost distance or no.of stoppages?

Harmanpreet Singh said: (Nov 24, 2013)  
As speed of bus without stoppage is 54 kms per hour (i.e) in 1 hr bus travels 54 kms.(as Distance = speed *time).

Similarly as speed of bus with stoppage is 45 kms per hour (i.e)in 1 hr bus travels 45 kms(as Distance = speed *time).

Comparing the cases we can see that bus with stoppage covers 9 km less than the bus without stoppages.

Now we know that bus covers,

54 kms in 60 mins (1 hr)
1km in 60/54 mins
9 kms ---------------------- 60/54*9 = 10mins.

So with original speed of 54 km/h, bus stops for 10 mins.

Dumi said: (Dec 18, 2013)  
Can it be solved using x and y?

Yash said: (Jan 3, 2014)  
I tried by this method:

- - - Speed Time Distance.
Stop : 54 1h D.
Non-S: 45 1-X h D.

D is common for both, so,

54 * 1h = 45*(1-x)h.

X = 1/5 hr ==> 12 mins.

What went wrong in this method.

Sonu Singh said: (Jan 9, 2014)  
Why we get 54 as denominator?

Kavya said: (Jan 27, 2014)  
As we have subtracted the two speeds, then it would result as 9 kmph!

If 54 kmph means for 1hr------> 54km.

So now 9 kmph means 1hr------> 9km right so the answer is 60min.

Aksh said: (Feb 2, 2014)  
Answer is coming 12 min,
s = d/t.

54 = d because t = 1hr given -------- 1,
s = d/t.

45 = 54/(t+1) ------- 2.
By solving we get 12.

Brijesh Kesharia said: (Feb 20, 2014)  
A car starts running with the initial speed of 40 km/h with its speed increasing every hour by 5 km/h. How many hours will it take to cover a distance of 385 km?

Dushanthi said: (Mar 4, 2014)  
@Brijesh Kesharia,

40 + 45 + 50 + 55 + 60 + 65 + 70 = 385.

So, it takes 7 hrs.

Sumit Dubey said: (Mar 6, 2014)  
@Dushanthi,

Is there any shortcut method for solving the same problem (Brijesh Kesharia's que. ) for more complex data?

Ashish said: (Apr 21, 2014)  
For all those who got answer as 12.

12 min is the stoppage time for (60+12) min i.e 72 min. So, for 60 min. i.e 1 hr it would be 60* 12/72=10 min.

Alok Kumar Mishra said: (May 6, 2014)  
54km less if it stop for 1 hr.

1km less if it stop for 1/54 hr.

9km less if it stop for 9/54 hr = 9/54*60 = 10 min.

Bala said: (May 21, 2014)  
Due to the stoppages it travelled 9km less. So
For 1 hr -> 54km.

t(hr) -> 9km.

t = 9/54 = 1/60 = 60/6 = 10min.

Arun said: (Jun 25, 2014)  
Why you have taken 54 and why not 45?

ARJUN SAHOO said: (Jul 18, 2014)  
See..the bus runs up to 54 kmph in 60m. in nonstop mode.

If 45km in stop mode, the bus will take 72 minutes to travel 54 km in stop mode.(60/45*54).

So here bus taking 12 more minutes to reach at the destination but in 72 minutes. As per question, in 60 minutes the bus will take extra minutes to halt => 12/72*60=10 proved. Answer is 10.

Saurabh said: (Jul 24, 2014)  
For those who got i2 min as answer.

Solve like this;

As distance is same....

54=d/(1-x).........(1) where x is the stoppage time.

45=d/1.............(2).

Solving eq 1 & 2,we get x=0.166 hrs. So in minutes ANS = 10.

Suresh said: (Aug 1, 2014)  
Excluding stoppages, the speed of a bus is 54 kmph.
Including stoppages, the speed of a bus is 45 kmph.

The difference between 54 and 45 is 9 that means the bus stopped.
Overall about 9 kms.

Formula : (Difference/Bigger value)*60.

Therefore (9/54)*60.

Lipu said: (Sep 24, 2014)  
If speed is 54 kmph.

So in one hour bus travels 54 km.

Again time taken by bus to travel 54 km with speed 45 kmph will be (54/45) *60 min=72 min.

So to reach at the same position more time required 12 min.

So 12 min is the stopped time.

Deba said: (Oct 30, 2014)  
Why we are considering 54 kmph rather 45 kmph?

Surendra said: (Jan 11, 2015)  
To all those who have doubt why 54 kmph is considered. The problem is to find how many minutes does the bus stops in stoppages.

54 kmph means it travels 54 km per a single hour (i.e 60 min) excluding stoppages.

Including stoppages speed reduced to 45 km per a single hour. It means per one hour due to stoppages there is 9 km loss per a single hour.

We should take 54 kmph because we should know what time it takes for bus for a km. So 54 km-->60 min then 1 km-->60/54 min.

For 9 km--> (9*60) /54 = 10 min.

Veeresh said: (Mar 26, 2015)  
Why we are considering 54 kmph rather 45 kmph?

Guna said: (May 9, 2015)  
Please explain in min to sec and min to hours.

SANDEEP said: (May 19, 2015)  
I will suggest one more formula to solve this kind of problems when stoppage time has to be calculated.

Then, stoppage time = 1-Slower speed/Faster speed.

Hence in this case.

= 1-45/54.
= 1- 5/6.
= (6-5)/6.
= 1/6.

Which can be converted to = 1/6*60 = 10 min.

Sukumar Satyen said: (May 20, 2015)  
Suppose bus will take t hours to cover certain distance, if there are stoppages, as we know speed = d/t = = 45kmph.

Total distance covered by bus = speed*time = 45t....equation(1).

If bus did not stop at those stoppages, where stoppage time was s hours, then bus actually saved s hours to cover same distance.

It means that due to travel time of (t-s) hours, the speed was increased, as we know speed = d/(t-s) = 54kmph.

Total distance covered by bus = speed*time = 54kmph*(t-s) = 54t - 54s...equation(2).

From equation (1) and (2),

54t-54s = 45t.

=> 54t-45t = 54s.
=> 9t = 54s.
=> 9t/54 = s.
=> s = t/6.

If t = 1 hour = 60 minutes,

Then, s = 60/6 = 10 minutes.

Sha said: (Jul 19, 2015)  
How can you take if t=1 randomly?

Aditya said: (Aug 25, 2015)  
There is a formula for this questions:

(V1-v2)/v1.

V1= Without stoppage velocity.

V2 = With stoppage.

Result is in hour. Multiply by 60 to get minutes.

Ronak Bhatia said: (Sep 12, 2015)  
For 60 min......54 kmph so.

For ? min.......45 kmph.

= 45*60/54 = 50 mins it means 10 mins less so it has stopped for 10 mins.

Just For You said: (Jan 8, 2016)  
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.

Somanka said: (Jan 18, 2016)  
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.

Deepika said: (May 5, 2016)  
Well said @Nitesh Nandwana.

It's simple and easy to solve.

Abc said: (May 23, 2016)  
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.

Nen said: (Jun 18, 2016)  
Hi, I'm not getting this. Can anyone explain me clearly?

Shubh said: (Jun 29, 2016)  
@Nen.

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

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

By solving this we get the answer.

S.V.R said: (Jul 28, 2016)  
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.

Tushar Mehta said: (Aug 7, 2016)  
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.

Swathi said: (Aug 9, 2016)  
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.

Pavan said: (Aug 12, 2016)  
Thanks, @Swathi.

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

Subhashini said: (Aug 15, 2016)  
How to came 9 kms and why we choose 54 kmph rather 45 kmph.

Farhat said: (Aug 19, 2016)  
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.

Prasanth said: (Aug 24, 2016)  
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.

Omega said: (Sep 23, 2016)  
@Sundar,

Can you explain in an easy way?

Veda said: (Sep 30, 2016)  
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.

Gangadhar said: (Oct 6, 2016)  
Bus A travels 54km in 60 min that means to travel 1km it takes(60/54) 1.11min.
Bus B travels 45km in 60min with stoppages.

Here, the speed of both the buses are same but bus B gives stoppages that's it.
i.e. both A & B bus covers 1 km in 1.11min only. So if bus B takes 1.11min to travel 1km then to cover 45km it will take 45 * 1.11 = 50min(actually travelled time without stoppages ).

So, the time T = travelled time with stoppages - travelled time without stoppages.
T = 60 - 50 = 10 mins.

Suyash More said: (Oct 12, 2016)  
Here distance is constant.

Let x be the time for which the vehicle speed.
Hence, 54 * (60 - x) = 45 * (60).......(s1 * t1= s2 * t2).
x = 10 min is the answer.

Ravi said: (Oct 19, 2016)  
Can anyone explain it clearly, please?

Saif said: (Nov 6, 2016)  
@Ravi.

We have been given speeds with stoppages and without stoppages,i.e., 45KM/h(with stoppages) and 54 Km/h( without stoppages).

Now, the question wants us to find that how much time is consumed in those stoppages.

Here the value of speed is based upon the time it took to reach a particular distance.

So naturally with stoppages the time will be more so for same distance the average speed is reduced i.e., 45Km/h.

Without stoppages, speed will be 54km/h.

Now consider the time to be one hour.Why one hour, because question wants us to find the minutes the bus stop per hour. Per hour.

So what is the distance for One hour at 54km/h and 45km/h?

Distance = 54KM and 45KM.
Now, what is the difference between these two?
9Km.
This is done to find what stoppages cost in term of distance between two buses.

Now, why 54Km?
Since you already know the difference in distance due to stoppages you need to use the speed with which the bus is covering that stoppage distance.

So,
9/54 = 1/6hr.
To convert this into minute just multiply it with 60 and you will have a number of minutes.,i.e., 10 Mins.

Is it clear now Ravi?

MMMMM said: (Nov 8, 2016)  
The speed of a train is 80 kmph and for every bogie added, the speed decreases by 10%. How many minimum numbers of bogies should be added to reduce the speed of the train to less than 50 km/h?

Can anyone tell me the answer?

Madan said: (Nov 24, 2016)  
Explanation:

Excluding stoppages (ES) - 54.
Including stoppages (IS) - 45.
Formula: (ES - IS)/ ES.
=> (54 - 45)/54 = 9/54 = 1/6 hrs (or) 10 mins.

Md.Tamheed Khan said: (Nov 25, 2016)  
Nice explained @Jaya and @Kaushal.

Kathleena said: (Dec 1, 2016)  
Car travels with an average speed of 70 km/hr from Magallanes interchange to bicutan in 5 mi how far are these two places? How fast is the car travelling after 2 mi?

Please sole this.

Manish Pillai said: (Dec 27, 2016)  
This can be done using allegations easily.

54 0
45
45 : 9

That is 5:1.

So, it should not travel for 1/6 of an hour that is 10 min.

Chaithu said: (Jan 3, 2017)  
Thank you for all your simple explanations.

Mir Rokon Uddin said: (Jan 16, 2017)  
His regular speed reduce 54k/h to 45k/h.
So we have to find out the missing time from the regular speed.
The difference of the distance is 9kmh.
So missing time = (1* 9/54) * 60min.
= 10min.

Shri said: (Jan 21, 2017)  
@Mmmmm.

5 bogies should be added.

Jadhav said: (Feb 3, 2017)  
It's very simple.

54 - 45\54 * 60 = 10 min.

Sambath said: (Feb 3, 2017)  
Super explanation @Jaya, @Kusal.

Rajesh.r.kzm said: (Feb 10, 2017)  
Excellent explanation @Jaya.

Yamine said: (Mar 19, 2017)  
Good explanation @Jadhav.

Bhavi said: (Mar 25, 2017)  
Great explanation @Kushal.

Shunail Ali said: (Apr 22, 2017)  
Great explanation @Kushal and @Jaya.

Jayawant said: (May 6, 2017)  
Speeds given : without stoppage 54km/hr and with stoppage 45km/hr.

Vehicle has to cover same distance.
Let us assume it travels distance 270 kms (LCM of 54 and 45).
With 54 km/ hr, total 5 hrs are needed and with 45 km/hr, total 6 hrs are needed.
It means with stoppage it has to stop for I hr in 6 hrs.

So, within 1hr, it has to stop for 1/ 6 hr i.e. 10 minutes.

Palash said: (May 27, 2017)  
Great explanation @Jayawant.

Blossom said: (Jun 28, 2017)  
How it came?

Sukhwinder said: (Jul 2, 2017)  
Right @Jaya.

Bharathi said: (Jul 14, 2017)  
Why we do not consider 45? explain.

Preeti said: (Jul 22, 2017)  
@Bharathi.

The main scenario is that, in one condition, the time taken by the bus for the stoppage in an hour, in another condition in that time the bus travelled some extra distance.

So, we have to calculate in how much time it travels the total extra distance i.e. 9 km and that is the time the bus spent on stoppages.

That's why we didn't consider 45.

Mandy said: (Aug 5, 2017)  
The average speed (including stoppage) is 45 km/hr.
Distance = (rate)(time).
So, in ONE hour, the distance traveled = (45)(1) = 45 km.

The average speed (excluding stoppage) is 54 km/hr.
At this speed, HOW long will it take the bus travel 45 km?
time = distance/rate.
So, time = 45/54.
= 5/6 hours,
= 50 minutes.

At a speed of 54 km/hr, the bus can travel 45 km every 50 minutes.
So, it must be motionless for the other 10 minutes.

Ramesh Nayak said: (Aug 9, 2017)  
The distance between A and B is 999km.The express train travels place A at 6 a.m. and runs at the speed of 55.5 kmph. The train stops on the way for 1 hour 20 minute.The train reaches B at?

Please solve this question.

Srijani said: (Aug 18, 2017)  
There is another easier method.

54 km is traveled in 1 hr
1 km------------- 1/54 hr
45 km---------- 1/54*45= 5/6 hrs.

Now, if we subtract the times, i.e 1 - 5/6 = 1/6 hr (we are subtracting this because 45 km should have been traveled in 5/6 hrs and not 1 hr. Hence, the time taken is more so subtracting, we get the no. of minutes the bus stopped).

converting to minutes 1/6 * 60 = 10 min.

Umakanta Langpoklakpam said: (Aug 22, 2017)  
Due to stoppages, the bus lags =(54-45)Kmph=9Kmph in speed.
So, time taken at each stoppages= Speed /original speed.
=9/54 hrs,
=9*60/54mins,
=540/54mins,
=10mins.

Vinayak Mahadev said: (Aug 28, 2017)  
Consider A and B two bus,

A with stoppages km/hr - 45
B without stoppage km/hr - 54

1 hour travel.
B far away from A.
that distance is 9 km.

Just think 9 km A don't stop in anywhere there speed is increased. Because A's is the Avg speed 45 km/hr.

Here we can't find the stoppage from A's speed
Go next option B,
from B the bus,
Easy to find out the time taken from 9 min travel that 9 min travel is A's stoppage time

So,
distance = time * speed,
54 km = 1 hour * 54 km/hrs,
if 1 km = time ? * 54km/hrs,
9 = t* 54,
1/6 = t (in hours),

In min,
1/6*60 =10min,

Ramaprasad said: (Oct 4, 2017)  
Can anyone clearly explain why we had taken 9/54 instead of 9/45?

Tiru said: (Oct 28, 2017)  
@All.

if ans 10mins, 54*60 = 45*(60+10) which is not correct
if ans 12 mins, 54*60 = 45*(60+12) which is correct
So ans is 12 mins, not 10 mins.

S R D said: (Nov 12, 2017)  
Ans is 12 min. Solve the problem by taking 10mins and then 12mins.

Niharika said: (Nov 26, 2017)  
@ALL.

The direct formula is (excluding-including*60/excluding).

Yash Soni said: (Dec 25, 2017)  
I'm not clear why we take 54. I think we take 45 because in 54 the bus is not stopped then how can 54 gives us the stoppage time?

If we take 45 so we get the answer (12).

Shriii said: (Jan 26, 2018)  
@Yash Soni.

If we take 45 then the bus is already stopped. And 45 is not the actual bus speed. It's the speed that is just calculated when the bus is stopped at stops. So 54 is its actual speed. So we should take 54.

Aria said: (May 5, 2018)  
How we will calculate ratio of travelling time and stoppage time in this question?

Surya said: (Jun 2, 2018)  
To cover 54km it takes 60 min, for 1 km time taken = 60/54, then for 45km time =(60/54)*45 = 50min, to cover 45km it just need 50min but it take 60min with stoppage, it take extra 10 min which means the bus stop for 10min.

Aman said: (Jun 20, 2018)  
Why is it written 150 instead of 50%?

Raj said: (Jul 6, 2018)  
Thank you @Kunal.

Lohith said: (Jul 12, 2018)  
We can do this simply by ratios.

Given speeds 54kmph,45kmph ratio:54:45,
Speeds ratio- 6:5.

Times ratio will be- 5:6 (since speed and time are inversely proportional).
In times ratio 1 part difference is there hence in total 6 parts 1 part is stoppage we calculate (1/6)*60=10.

Priya said: (Aug 15, 2018)  
Thank you @Lohith.

ACHYUT KUMAR PATRA said: (Aug 29, 2018)  
I think 10 is the right answer. I agree with the given answer.

Naidu said: (Sep 8, 2018)  
Well said @Bipana.

RAJU said: (Nov 8, 2018)  
Bus can cover distance without stops for 60mins(60 * 54) = 3240m.
Bus can cover distance with stops for 60mins (60 * 45) = 2700m.
difference distance = 540m.

Time = distance/speed = 540/54 = 10mins.

Borade Vikas said: (Nov 12, 2018)  
How we take the ratio of (9÷54)*60?

Please explain this step.

Sahil said: (Nov 14, 2018)  
Let 54 km and 45 km is a distance that travelled by bus in *1hour*.

45 km distances travelled by car in 1 hour due to the stoppage.
If it travels without a stoppage, it would cover in a 45km/ 54kmph = 5/6h.
5*60/6 = 50 min,
60-50 = 10 minutes.

Ram said: (Dec 8, 2018)  
Let the distance be 270 km.
During normal speed, i.e 54 km/hr. The time taken =5hrs.
And with the average speed of 45 km/hr, the time taken is 6 hrs, i.e 60 minutes more.
My doubt is that these 60 minutes must have been spending in the interval of 5 hrs, i.e 12 minutes per hour.
Why can't the answer be 12 minutes?

Karthik said: (Dec 21, 2018)  
Simply, the solution is;

60min --> 54km
x min --> 45

>>x=50;

This means with stoppages it is taking 50 min to reach 45km.
but now without stoppage it is taking 60 min so with stoppage it is taking extra 10 min.

Manjiri said: (Dec 28, 2018)  
See I will reframe the question to understand it in a better way.. Bus has started from point A. there are stops in between till point B so its speed is less i.e. 45km/hr. Now after this point there are no stops so it increases its speed to 54km/hr to reach point C. We have to find the time lapse of distance covered between these two speeds. lets find the distance 1st.
s=d/t.
let's say time taken be 1hr. so acc to this distance covered till point B is 45km
n from B to C is 54km
So, the distance gap is of 9km.

Now the time lapse for this distance we have to find. the extra distance from B to C is covered with speed of 54km/hr.
Thus, t= 9/ 54 is 1/6 hr.
So 1/6hr * 60 = 10 mins.

Divya said: (Jan 5, 2019)  
Thanks for the answer @Jaya.

Ranjeet Bind said: (Mar 30, 2019)  
Let's suppose,

Excluding stoppages speed (s1) and including stoppages speed (s2)
then;

The stoppage minutes per hour = (difference b/w the speed(s1~s2))/(Excluding stoppages *60 minute speed (s1)).

Gangadhar said: (May 23, 2019)  
(Without stoppage-with stoppage)/Without stoppage.

(54-45) /45.
(9/60) *60.
10 min.

Basil said: (Jun 4, 2019)  
Can't we consider like taking the ratio of speed and time since distant is constant, time is inversely proportional to speed?

From which we can get the ratio of stoppage to total travel time. Please explain to me.

Sarah said: (Jun 22, 2019)  
There's a formula for this type of ques:

Speed of bus (excluding stoppage) - Speed of bus (including stoppage) * time/ speed of bus (excluding stoppage).

If you put values in this formula:
Speed of bus without stoppages= 54-45 = 9km/hr,
Time = 1 hr.
So, distance without stoppages = 9 *1= 9 km.

[(54-45) / 54] * 60 = 10.

We have taken the difference of speeds of excl and incl stoppages because we want distance without stoppages. We have taken 54 as denominator because the bus has stopped. We have multiplied it by 60 because the options are in minutes and we were getting answer in hours. If we had options in hours, so we won't have needed to multiply 60.

VenkataSiva said: (Jun 29, 2019)  
(Relative speed/maximum speed) * 60min.

Prithvi said: (Sep 7, 2019)  
For 54 km it is 60 min.
For 45 km how much?

54 = 60
45 = x
X = 50, the difference in time 10 min gives us stoppage time.

Aiswarya said: (Sep 10, 2019)  
Thanks @Prithvi.

SWADHIN said: (Sep 25, 2019)  
Very simple, thanks @Prithvi.

Sasinath said: (Dec 16, 2019)  
54-45 = 9kmph. i.e., the bus would lose 9km in 1 hr.

Let the time bus stops at a time be t. Then the distance bus would lose will be s. Then s will be,

s = v*t = 54*t.

Let a total number of stoppages be x.

Then the total distance lost by the bus in the second case is,

x*s = x*54*t.

x*54*t = 9.

x*t = 1/6.

So in 1 km, t = 1/6 hour = 10 mins.

Satwik said: (Jan 4, 2020)  
For 1hr ---> 54km.

For how much time with 45km/hr it takes to travel 54km is the total time taken by the bus to travel with stops.

So t=(54/45)*60=72min;.

Its the total time taken subtracting an hour travelled common and we get 12 min.

then how come 10 min be the answer?

Sabbir said: (Jan 8, 2020)  
Travelling difference = 9 km/hr.

Travels 54 km taking 60 mins.
Hence, travels 9 km taking 10 mins.

So, the answer is 10 mins.

Pallavi said: (Jan 11, 2020)  
We have taken 54 because if we take 45, this is the speed of bus with the stoppage, it has already taken the stop that's why 54 is taken.

Bantu Venkatesh said: (Jan 17, 2020)  
54km ------------- 60min
45km ------------- ?????.

45/54*60min = 50min.
60min - 50min = 10min.

KArthik said: (Jan 18, 2020)  
Thank you @Kushal.

KArthik said: (Jan 18, 2020)  
Hey guys, for this we can simply use the proportion method;
60min : 54km :: x min : 9km (product of extremes = product of means)
60*9=54x.

x=(60*9)/54 (9 and 54 will be cancelled by 9 tables)
x=60/6 (60 and 6 will be cancelled by 6 tables)
x=10min.

Therefore, the time taken by train is 10 min.

Anvi said: (Mar 3, 2020)  
Can anyone tell me the easy method.

Bhavya said: (May 7, 2020)  
2 speeds difference is 9 km,
So we should calculate the time taken to cover 9 km.
So, 9/54*60 =?
Then the answer is 10 minutes.

Sravani said: (Jun 1, 2020)  
You were excellent! Thanks, @Jaya and @Kushal.

Kumar said: (Jun 6, 2020)  
I didn't understand, I'm confused about this stoppages can anyone explain in detail?

Chandu said: (Jul 5, 2020)  
Stoppage time = difference of speed/maximum speed.
= 54-45/54 * 60min,
= 9/54 * 60min,
= 1/6 * 60min.
= 10min.

Boss said: (Jul 22, 2020)  
Good explanation, thanks @Jaya.

Donald Trump said: (Jul 25, 2020)  
Here, the confusion is how come 45/54?

However, the main thing to be noted is that the bus travels at 54kmph in both cases. However, due to stopping for some time, the average speed becomes 45 in case 2. Whereas in the first case, the 54kmph average is the same as its speed because it never stops.

So considering one hour of time, the bus itself covers 45km instead of 54km. We have a difference of nine kilometers in the distance traveled. But we cannot used the average speed of 45 since it travelled at 54 irrespective of the case.
So 9/54 becomes 1/6 hours or 10 minutes.

Joel said: (Sep 25, 2020)  
Without stops, Bus travels - 54 Km in 1 hr.
With stops, the bus travels- 45 Km in 1 hr.

So the extra distance the bus could have travelled if there weren't any stops= 54-45=9 Km.
So the time is taken for travelling that 9 Km is the same as the time taken for the stops,
V = d/t.
54 = 9/t.
t = 9/54 hrs=(9/54)*60=10 min.

Prerna23 said: (Oct 5, 2020)  
The LCM approach here makes our work easy. This can even be applied in problems on pipes and cisterns, work and time, etc.

So, first, take the LCM of 54 and 45 to be the distance covered i.e. 270 km.

The time taken without stoppage is 270/54 = 5 hrs. The time taken with stoppage is 270/45 = 6 hrs. This implies that out of 6 hrs, 1 hour accounts for the stoppage because 6-5 = 1.
Next, apply the unitary method.

6hrs ---------- 1 hr of stoppage.
1 hr ----------- (1/6)*60 = 10 mins stoppage.

Analogously, in case of pipes and cisterns, the lcm of the time taken by the pipes to fill/empty can be taken as the total capacity of the cistern.

Sangay Wangdi said: (Oct 6, 2020)  
54 km in 60 minutes.

9km in x.
Cross multiply.
60 * 9 =540/54.
Is equal to 10 minutes.
So, 9km is taking 10 minutes to stop.

Vishnu said: (Dec 7, 2020)  
Let me try it in my way
A Particular Distance is travelled by the Bus at 54kmph

When stoppages are included, 54 kmph turns to 45kmph in order to compensate the increase in time.

Let Distance = D, time = t, increase in time = x

D = 54 * t ---> (1)
D = 45 * (t + x) ---> (2)

Equating (1) & (2)

54t = 45 (t+x).
54t = 45t + 45x,
9t = 45x,
9t/45 = x,
(1/5) t = x,
t = 5x.


We need to find x for 1 hr (60 mins)
i.e t+x = 60.
5x+x = 60.
6x = 60.
X = 10.

(Some friends are getting 12mins instead of 10 mins because they are taking (t = 60 min) but (t +x = 60) is the correct one.

Umer said: (Feb 25, 2021)  
1hr distance without stoppage = 54km,
1hr distance with stoppage = 45km,
=> distance difference = 9.
9/54*60=10.

Nevil K Joseph said: (Apr 5, 2021)  
Simple:

The Speed of a bus without a stoppage is 54kmph.
The speed of bus with a stoppage is 45kmph.
So from this, it is clear that the speed of the bus is 54kmph only;
Now think like this;

54 mango costs 60 rs (1hour = 60minutes);
So 1 mango costs (60/54)rs.
Here the bus travels 9 km less in one hour due to stoppings,
Therefore 9 mango costs = (60/54)*9.
i.e. = 10 rs or 10 minutes.

Karthik said: (Aug 3, 2021)  
The bus travelled only 45kms. Hence, it would be correct to divide 45 (and not 50) and multiply 60 with 9 kms (less travelled).

Am I right? please clarify for me.

Hema said: (Aug 24, 2021)  
Bus travels at 54 km/hr.
Due to stoppages say t min, it travels only for (60-t) min.
(60-t) min= (60-t)/60 hr,
Given average speed = 45 km/hr,
Average speed = distance travelled/ total time taken.

45 = (54*(60-t)/60)/1 hr.
45 = 9*(60-t)/10,
450 = 540-9t,
t = 90/9 = 10 min.

Umar said: (Sep 16, 2021)  
Non stoppages speed= 54kmph,
with stoppages speed= 45kmph.

Reduce speed due to stoppages = 54-45 = 9 kmph.
we need to find the time taken by bus at a stop in each hour i.e t
t = s/v,
t = 9/54 ph ( we take 54 because we are talking about non-stoppages).
= 1/6 *60 min.
=10 min.

Harsh said: (Sep 21, 2021)  
@Sumit Dubey.

Use Arithmetic Progression (A.P.)
Sum to n-terms = n/2(2a + (n-1)d).
n/2 (2*40 + (n-1)5) = 385
40n + 5n^2/2 - 5n/2 = 385
5n^2 + 75n - 650 = 0
(5n - 35)(n + 21) = 0.

So,
n = 7 or n = -21.
As n (time) cannot be negative we will discard -21.
Hence, the answer is 7 hours.

Ramesh said: (Oct 19, 2021)  
Let's we take that a bus reach an 54 km distance in 1 hour without any stoppages while the bus was covered 45 distance with some stop.

So we can understand that the remaining 9 kms were not reached the bus.
So, 9 km travelling time will be a stop time. We all know that, time=9/54*60=10 mins.

SABHU said: (Dec 8, 2021)  
Min per hour= (difference of two speeds÷ without stoppage)*60.
Or
Min per hour=(diff of two speeds÷ large number)*60.

Johnty said: (Mar 7, 2022)  
Why we take 54 instead of 45? Please explain.

Bantu said: (May 16, 2022)  
54km -------- 60min
9km ----------- ?min


Then, 9km÷54km * 60min = 10mints.

Suraj said: (Jun 14, 2022)  
Thanks for explaining @Anoo.

Thomas K Mathai said: (Jul 7, 2022)  
@All.

Consider the distance is only 54 kms. At 54 kmph it will take only 1 hr.
But since due to stoppages it takes 10 minutes extra (the time of stoppages).
So, shouldn't we get 45 kmph if we divide 54 km the distance by 1 hr 10 minutes (70 minutes)? We don't get that, of course. The bus runs at 54 and with the stoppage, rit reaches 45 km. 9 km is remaining. The average speed with stoppages was 45kmph. the remaining distance of 9 km has to be completed by that average speed as there are no more stoppages to get the correct time taken by the bus and not by 54kmph.

So, it will work out to be 12 minutes, not 10 minutes.

AzadShankar said: (Sep 9, 2022)  
Speed is 54 km/hr, here clarity is speed is never reduced.

So in one hour, it covers 54 km without stopping, now since it has stopped it covered only 45 km at speed of 54 km/hr. had it not stopped it would have covered 54 kms, but it stopped hence it covered only 45 km.
Distance not covered is 54 - 45 = 9kms.
Now the time it would have taken to cover 9kms is (time = distance/speed)
Time reqd to cover 9 km @ 54km/hr = 9/54 = 1/6 hours i.e 10 minutes.

Prathamesh Kadu said: (Sep 23, 2022)  
(Initial - final/initial) hours = covert to minute and get the answer.

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