Two vehicles A and B leaves from city Y to X. A overtakes B at 10:30 am and reaches city C at 12:00 pm. It waits for 2 hrs and return to city Y. On its way it meets B at 3:00 pm and reaches city Y at 5:00 pm. B reaches city X, waits for 1hr and returns to city Y. Afer how many hours will B reach city Y from the time A overtook him fro the first time?

1) 50 hrs
2) 49.5 hrs
3) 41.5 hrs
4) 37.5 hrs

• suppose distance b/w x&y=a
  since after reaching at x;A start at 2:00 and reach at y at 5:00
  speed of A=a/3
  since in coming from y to X A overtook B at 10:30 and reach at X at 12:00
  so in 1.5 hours it will cover half distance of YX=a/2
  again in returning from X to y it meet B at 3:00 so distance from X to here=a/3
  means distance from Y to 2nd meet of B=2a/3
  so B covered distance in 4.5 hours(3:00-10:30)=2a/3-a/2=a/6
  since B covers a/6 in 4.5 hours
  so B will cover distance a in (4.5/(a/6))*a=27 hours
  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
  so correct option is (3)
• 10 years agoHelpfull: Yes(32) No(2)
• is this a tough question?
• 9 years agoHelpfull: Yes(8) No(1)
• 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
• 8 years agoHelpfull: Yes(2) No(2)
• @ASHVINI KUMAR
  how did you get the halt time for 1hr pls explain
• 10 years agoHelpfull: Yes(0) No(0)
• @Niveditha Ravichandran.....its given in the question " B reaches city X, waits for 1hr and returns to city Y"
• 10 years agoHelpfull: Yes(0) No(0)
• explain
  it
  
• 9 years agoHelpfull: Yes(0) No(0)
• It should be reaches city X at 12:00 pm and not city C
• 7 years agoHelpfull: Yes(0) No(0)