advita wrote:A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?
5 minutes
6 minutes
8 minutes
9 minutes
10 minutes
source-gmatclub.
oa-....b 6 min.
Great Question, Thanks for posting such a question.
In all there are three people different items moving, Two in the same direction and one in opposite direction.
Ist
Let the cyclist be moving in clock wise direction.
IInd
Those Buses which overtakes cyclist in every 12 minutes, They must also be moving in clock wise direction.
IIIrd
Those Buses which meet cyclist from the opposite direction in every 4 minutes, They must be moving in anti clockwise direction.
Let the Speed of cyclist be
C
Let the Speed of Bus in clockwise direction or in the same direction in which cyclist is traveling be
X
Let the Speed of Bus in anti clock wise direction or in opposite direction in which cyclist is traveling be
X
Speed of the Both of the Buses is same,
I have not even started the problem and it is still very lengthy.... 
Distance is Constant, by the Formula Speed = Distance / time,
C + X = 1/4
X - C = 1/12
On solving Both X = 2C
This means the speed of Bus is twice the speed of cyclist
I used options after that
Just mark three point on the Circle like
--------------------9----------------0----------------1/3--------------------2/3----------------------1------------------
Now buses at point
9 , 0 & 1 on the circle and our cyclist is at 0 point Or we can consider them as bus stops.
While Going from 0 to 1 cyclist will meet the buses coming from anti clock wise direction is 1/2
So the time for which cyclist travel in 4 minutes and that is exactly the same time that the bus travel from 1 to 1/2
If Bus takes 6 minutes from bus stop to next stop. Cyclist must take 12 minutes to cover the same distance.
in 4 minutes cyclist will cover 1/3 of the distance and Bus will cover 2/3 of the distance
and The Bus that is at 9 Will cover the distance of two bus stops in 12 minutes and the cyclist will the distance of from one bus stop to the second...
Hence Interval of Bus is 6 minutes....
