Two vehicles A and B leave from Y to X. A overtakes B at 10:30 am and reaches X at 12:00. It waits for two hours and returns to Y. On its way, it meets B at 3 PM and reaches Y at 5 PM. B reaches city X waits for 1 hour and returns to y After how many hours will B reach to Y from the time A overtook him.

• Let distance between A and B be d.
  A reaches X at 12:00 waits for 2 hrs and return to Y at 5pm.
  Hence speed=dist/time=d/3.....(1)
  
  
  Now during Y to X he overtakes B at 10:30 and reaches X at 12:00.
  Its takes 3 hrs to complete whole distance then in 1:30hrs he should complete Half the distance.
  
  therefore distance from Here to X will be d/2.
  
  Again in return journey he meets B at 3:00 so distance covered should be 1/3
  
  Here distance from X to here is d/3.
  
  Therefore distance covered by B is d/3-d/2=d/6.
  Time taken=4.5 hrs
  
  So B will cover distance d in 4.5*6=27hrs.
  
  after meet to A 1st time ,B covers total distance=a/2+a(wait at X)
  so total time =27(from X to Y)+27/2(after meeting A 1st time to reach at X)+1(halt at X)=41.5
  
  Therefore answer is 41.5hrs
  
  Explaination:
  
  |--------------------d------------------------------|
  Y---------------------------------------------------X
  10:30 3:00
  |-----d/3--------|
  |-------------------||----------d/2------------------|
  |--------S-----|
  
  S=d/3-d/2=d/6 in 4.5hrs
  
• 10 years agoHelpfull: Yes(48) No(5)
• Let the distance between City X and Y be D
  As given - B leaves City X at 2:00 (12:00 + 2 hrs halt) and reaches City Y at 5:00
  
  So it takes him 3 hours to cover distance D.
  
  Now, A overtakes B at 10:30 and reaches city Y at 12:00 pm , which means that A traveled for 1:30 hr.
  
  Now see,
  A takes 3 hrs takes to cover distance D
  so in 1.5 hrs A will cover D / 2 distance
  
  Now see another part -
  "On its way, it meets B at 3 PM and reaches Y at 5 PM."
  Given that - B leaves City Y at 2 PM
  So distance covered by A in 1 hr (3 - 2) = D / 3
  
  Now Total Distance covered by B during (A overtaking B + A wait for two hour + A on its way back ) is
  
  D / 2 [when they first overtake] - D / 3 [when they again overtake]
  = D / 6
  
  Now Time elapsed during this period (A overtaking B + A wait for two hour + A on its way back )
  =1.5 + 2 + 1
  =4.5
  
  so to cover D / 6 distance B took 4.5 hr
  to cover D distance B will take (4.5 * 6)
  = 27 hr.
  
  Now "After how many hours will B reach to Y from the time A overtook him."
  Time to reach X after A overtook (D / 2) + wait + Time to reach Y from X (D)
  = 13.5 + 1 + 27
  = 41.5
  
• 10 years agoHelpfull: Yes(21) No(1)
• ans is 41.5hrs... please refer to tcs seesame
• 10 years agoHelpfull: Yes(2) No(0)
• 35 hours..
  ??? not sure!!
• 10 years agoHelpfull: Yes(0) No(4)
• 5.5 hr because B also wait for an hour at X
• 10 years agoHelpfull: Yes(0) No(2)
• 5.5 hr because B also wait for an hour at X
• 10 years agoHelpfull: Yes(0) No(1)
• tcs ans 41.5 hours
• 10 years agoHelpfull: Yes(0) No(1)
• ANUJ YADAV how it is comming "Therefore distance covered by B is d/3-d/2=d/6.
  Time taken=4.5 hrs" plz xplain
• 10 years agoHelpfull: Yes(0) No(0)
• 35 ??
  pls correct me
• 10 years agoHelpfull: Yes(0) No(0)
• ans 40.5
  
  
• 10 years agoHelpfull: Yes(0) No(0)