Excluding stoppages, the speed of a bus is 54km/hr and including stopp

We are given that speed of the Bus with stoppage is 45km/hr. Which means the Bus actually travels 45 km in an hour. This does not mean the bus actually travelled for full 60 minutes, because it is given that the bus had stoppages.

Now the duration in an hour the bus actually travels, the speed of the bus during that duration is 54km/hr.

So let's say the bus actually travels for T minutes in an hour. From the given information we can say

54 * T/60 = 45
T = 45 *60/54 = 50 minutes.

So the duration of the stoppage in 1 hour = 60 - 50 = 10 mins.

Answer is B)10

Solution:


Let the total distance the bus travels be d. Let the bus travel for t hours in total and stop for s hours in total. Notice that the speed of the bus is d/t excluding stoppage and d/(t + s) including stoppage. Setting the first expression equal to 54, we obtain:

d/t = 54

Similarly, setting the second expression equal to 45, we obtain:

d/(t + s) = 45

Let’s rewrite the first equation as d = 54t and substitute this expression for d in the second equation:

54t/(t + s) = 45

54t = 45(t + s)

54t = 45t + 45s

9t = 45s

t = 5s

Now, notice that the ratio of the time the bus stops to the total travel time is s/(t + s). Substituting t = 5s, we see that the bus spends s/(5s + s) = s/6s = 1/6 of every hour stopping, which is equivalent to 60 * 1/6 = 10 minutes of stopping each hour.

Answer: B

let m=minutes per hour train is not stopped
45/54=m/60
m=50
60-50=10 minutes per hour train is stopped
B

Posted from my mobile device

This question can be done using unitary method:

54-45=9 mins

[(9/54)*60]mins=10mins

Hence, B

dendenden

Think about this - What you got is the time for which it stops in a period of 72 mins. What you actually need is the time for which it stops in a period of 60 mins. That brings you to an answer of 10 mins.

Check out my one minute solution to such a question by using weighted averages here: https://youtu.be/6Xjj5V2lxBg

Let's simplify it.. it took me a while to understand what the question wants (decode the question)... it's a little confusing..
in 1 hr, for how much time does the train stop?
fine.. so the train is actually travelling @ 45 km/hr (average) .. it includes stoppages too (Rest + Motion or R + M) and 45 km --> 1 hr which is why we choose 45 km... (first note).. secondly.. 54 km => Motion so, for 45 km (-> 1 hr) the train is in motion for 5/6 hrs => in 1 hr (-> 45 minutes) the train stops for 1/6 hrs = 10 minutes. simple..

Simple shortcut formula for approaching this question will be : Difference of speed / Speed without stoppage = 9/45*60 = 10, Answer must be (B)

It comes out to 12 mins according to your calculations.

Posted from my mobile device

54-45= 9 km less in 1 hour

Time taken to cover 9km with speed of 54km/hr

Time = distance/speed

9/54 =1/6 hr

=1/6 ×60 = 10 min

Posted from my mobile device

Hi, I did the reverse where I made the distance = 54 km in 60 mins. then used this to calculate for the time if speed is 45 (54/45 = 6/5 hrs). I got 72 mins. So 72 - 60 = 12 mins.

Is there an error in my calculation hence why I didn't get the correct answer of 10 mins. or is this not a correct logical solution? I figured I would get the same answer when done in reverse but somehow I didn't..? Can someone help explain please? Thank you.