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?

(a)5 minutes (b) 6 minutes (c) 8 minutes (d) 9 minutes

• ans: 6
  solution:
  Let's say the distance between the buses is d. We want to determine Interval=d/b, where b is the speed of bus.
  
  Let the speed of cyclist be c.
  
  Every 12 minutes a bus overtakes cyclist: d/b−c=12, d=12b−12c;
  
  Every 4 minutes cyclist meets an oncoming bus: d/b+c=4, d=4b+4c;
  
  d=12b−12c=4b+4c, ==> b=2c, ==> d=12b−6b=6b.
  
  Interval=d/b=6b/b=6
• 9 years agoHelpfull: Yes(14) No(14)
• http://www.veritasprep.com/blog/2012/08/quarter-wit-quarter-wisdom-some-tricky-relative-speed-concepts/
• 9 years agoHelpfull: Yes(6) No(0)
• two buses distance=d, and b=speed of buses
  
  12 minutes overtake therefor,
  d/(b-c)=12 ......(i)
  every 4 minutes he meets an coming bus,
  thus, d/(b+c)=4.....(ii)
  
  solving (i) and (ii),we get
  
  b=2c
  
  putting this in eq (i),
  
  d/b=6 (ans)
  
• 9 years agoHelpfull: Yes(5) No(0)
• Let's say the distance between the buses is d. We want to determine Interval=db, where b is the speed of bus.
  
  Let the speed of cyclist be c.
  
  Every 12 minutes a bus overtakes cyclist: db−c=12, d=12b−12c;
  
  Every 4 minutes cyclist meets an oncoming bus: db+c=4, d=4b+4c;
  
  d=12b−12c=4b+4c, --> b=2c, --> d=12b−6b=6b.
  
  Interval=db=6bb=6
  
  Answer: B (6 minutes).
• 9 years agoHelpfull: Yes(4) No(8)
• Let's say the distance between the buses is d. We want to determine Interval=db, where b is the speed of bus.
  
  Let the speed of cyclist be c.
  
  Every 12 minutes a bus overtakes cyclist: db−c=12, d=12b−12c;
  
  Every 4 minutes cyclist meets an oncoming bus: db+c=4, d=4b+4c;
  
  d=12b−12c=4b+4c, --> b=2c, --> d=12b−6b=6b.
  
  Interval=db=6bb=6
  
  Answer: B (6 minutes).
  
  
  
• 9 years agoHelpfull: Yes(3) No(3)
• option (c) 8 minutes
  two buses distance=d, and the interval time=d/b where b=speed of buses
  12 minutes overtake therefor, d/b-c=12 ......(i)
  every 4 minutes he meets an coming bus, thus, d/b+c=4.....(ii)
  equation (i) and (ii),we have
  d/b+d/b=12+4
  d/b=8(ans)
• 9 years agoHelpfull: Yes(1) No(2)
• thanks sanjay gupta for providing such a valuale site.... can u give some other sites which will be useful for elitmus
• 9 years agoHelpfull: Yes(1) No(1)
• Ans is 8.
  Let b be the speed of bus , c be the speed of cyclist.
  b - c : b + c = 12 - 4 : 12 + 4 = 8 : 16 = 1:2
  => c = 1b/3
  This means that the bus travelling at a relative speed which is 2/3rd of its usual speed (b-c = 2b/3)
  2/3 * 12= 8
• 8 years agoHelpfull: Yes(1) No(0)
• in the above solution why are you not adding the speed of two buses in the last when 6b/b i think there should be 6b/(b+b)
• 9 years agoHelpfull: Yes(0) No(1)
• b-c/b+c=4/12 : c=b/2 : so that relative time of bus =b-c = b-b/2= b/2
  so that total time taken = (1/2)*12= 6 min
  
• 8 years agoHelpfull: Yes(0) No(0)
• The time ration between them is 3:1,
  so the speed ratio will be inverse that is 1:3
  i.e (b-c):(b+c)=1:3(relative speed between them)=(1/2)b=c,
  the relative speed of bus will be(1-1/2)b=(1/2)b
  since b is constant then (1/2)*12=6 minute
  
  
• 8 years agoHelpfull: Yes(0) No(1)
• ans is
  c=(8 mins)
  
• 8 years agoHelpfull: Yes(0) No(0)