Aptitude - Time and Distance - Discussion

Why have we taken the speed of the train without stoppages (that is 54kmph) for calculating the time taken by the bus to cover 9 km?

Anyone, please clarify.

12 km is the right answer.

@Shravani.

Here is my explanation for your doubt.

It doesn't represent the actual speed, it includes the stoppages to cover less speed. Using 45kmph does not give us the correct answer that's why we use actual speed to find the time taken.

@All.

Very easy approach:

S1 = 54.
S2 = 45.

By ratio method:
The speed diff is 9kmph.
distance = 9 km.
T= d/s.
t = 9/54 = 1/6 hr=(1/6) * 60min.
t = 10 min.

See, the problem is simple, but we just require a way of understanding it.

Speed is 54kmph. That is clear. Now it says that due to the inclusion of 'stoppage' it is 45kmph. We need to understand that this just means that it appears to be 45kmph due to stoppage, which further means that where it had the potential of covering 54km in 1hr, it is now covering 45km in 1hr (but the speed is going to remain, just that the bus stops, hence time is consumed there, otherwise the speed is same only).

So (actual speed)*(1hr - time wasted due to stopping) = 45

Actual speed = 54kmph, and the time wasted has to be found out.

1hr - wasted time shows the effective moving time, due to which, while travelling at 54kmph, the bus covered a 45km distance only.

I hope it clears the doubt.

Well-said. Thanks all.

Ok, thanks for your explanation, it's helpful for me.

v1 = 54km/hr.
v2 = 45km/hr.
Relative speed = v2 - v1 = 9km/hr.
x min = 9km/hr.
60min = 54 km/hr.
x = (9 * 60)/54 = 10min.

I am not getting solution clearly. Anyone please help me.

1 hour is important.

Let's assume there is two versions of the bus. A version of the bus with a speed of 54 km per hour covers a 54 km distance, while a B version of the bus with a speed of 45 km per hour covers 45 km in 1 hour. Now imagine.

Represent 1 hour duration, --- represents the distance covered by A in 1 hour, and *** represents the distance covered by B in 1 hour and +++ is the extra distance travelled by A within 1 hour.

@ Naren.

Hence, 9 km is the extra distance covered by 'A ' version of bus in 1 hour, so now, the extra time of the bus A version is 9 /54 of 1 hour i.e. 1/6 th of 1 hour was used for extra distance to cover by version A of bus, hence this 1/6th of 1 hour was used by B version of bus for stopping at stops.

(Relate now A to B version of bus) That's why 54 km per hour was used.