Bus & cycle

crackgmat007 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
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?

GMAT club

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