Aptitude - Time and Distance - Discussion
Discussion Forum : Time and Distance - General Questions (Q.No. 5)
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?
Answer: Option
Explanation:
Due to stoppages, it covers 9 km less.
| Time taken to cover 9 km = |  |
9 | x 60 |  min |
= 10 min. |
| 54 |
Discussion:
206 comments Page 3 of 21.
Srijani said:
8 years ago
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.
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.
Nevil K Joseph said:
5 years ago
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.
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.
(5)
Abc said:
9 years ago
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.
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.
Milli said:
2 years ago
54kmh means it travels 54 kms in one hour when the train runs continuously in that hour. However including stoppages the train travels only 45 km in one hour. Thus in one hour train travels 9 km less due to stoppages.
Thus the time the train stops in an hour is the time it would have used to travel 9kms with the speed of 54kms, which when converted to minutes is equal to 10.
Thus the time the train stops in an hour is the time it would have used to travel 9kms with the speed of 54kms, which when converted to minutes is equal to 10.
(9)
Supreeth said:
1 decade ago
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.
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.
Jayawant said:
9 years ago
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.
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.
Sam said:
2 years ago
S1 = 54kmph
S2 = 45kmph
T=?.
D = S2-S1=> 54 - 45 = 9km.
# Due to stoppages it travels 9km less than its usual distance,
Time = Distance/Speed.
= 9/54 (S2 speed is taken to calculate the stopping time)
=1/6hr.
# To convert hr to min "*" by 60=>(1/6)*60 = 10min.
Therefore it stops 10min every hour in stoppages
Time = speed/distance.
S2 = 45kmph
T=?.
D = S2-S1=> 54 - 45 = 9km.
# Due to stoppages it travels 9km less than its usual distance,
Time = Distance/Speed.
= 9/54 (S2 speed is taken to calculate the stopping time)
=1/6hr.
# To convert hr to min "*" by 60=>(1/6)*60 = 10min.
Therefore it stops 10min every hour in stoppages
Time = speed/distance.
(40)
Just for you said:
10 years ago
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.
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.
Preeti said:
8 years ago
@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.
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.
Sasinath said:
6 years ago
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.
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.
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