Bus & cycle

[crackgmat007]

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
8
9
10

OA - B

[fruti_yum]

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
8
9
10

OA - B

Dont know what consecutive buses are.. are these oncoming or going buses? the question seems too vague.. what is the source?

[crackgmat007]

GMAT club

[vaibhav.iit2002]

here all buses are coming at same speed - from both directions

let say speed of bus=b, speed of cycle=c, time interval bet. consecutive buses=t

now if cycle wasn't moving and distance between first bus and cycle=s, then

s=bxt ...1
now when cycle is moving, its relative speed for an upcoming bus will be b+c and that for the other direction bus will be b-c

now s=(b+c)x4 and s=(b-c)x12

solving these eq, b=2c => s=3bx4/2=6b

from 1, bxt=s=6b, hence t=6

Ans. B