Aptitude - Time and Distance - Discussion

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?

@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?

Can anyone explain it clearly, please?

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.

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.

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.

@Sundar,

Can you explain in an easy way?

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.

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.

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