A and B started from the same point on a circular track. The ratio of their speed is n:1 (n is a whole number). If 5th and 17th time they meet at the same point, what can not be the value of n?
A) 2 B) 3 C) 4 D) 6

• Answer is n=6.
  
  If speed of two bodies moving in same direction in circular path are in the simplest ratio of a:b, then no:of pts they will meet = (a-b) provided a>b.
  Let circumference of circle be 'L'.
  Time for 1st meeting at any of the (a-b) pts = L/(a-b).
  Time for 1st meeting at Starting Pt = LCM of (L/a, L/b).
  
  Time for nth meeting at Starting Pt =n* LCM of (L/a, L/b).
  
  When n = 2 :
  a=2,b=1.
  No:of meeting pts = (2-1)=1pt.
  Only meeting pt is L.
  Time for first meeting = L/1.
  Time for first meeting at starting pt = LCM of (L/2, L/1) = L.
  Time for 5th meeting = 5L.
  Time for 17th meeting = 17L.
  
  Both tyms, they meet at pt L.
  So, n=2 is valid.
  
  When n = 3 :
  a=3,b=1.
  No:of meeting pts = (3-1)=2pts.
  Meeting pts are : L/2, L .
  Time for first meeting = L/2.
  Time for first meeting at starting pt = LCM of (L/3, L/1) = L.
  Time for 5th meeting = 5*L/2.
  Time for 17th meeting = 17*L/2.
  
  Both tyms, they meet at pt L/2.
  So, n=3 is valid.
  
  When n = 4 :
  a=4,b=1.
  No:of meeting pts = (4-1)=3pts.
  Meeting pts are : L/3, L/2, L .
  Time for first meeting = L/3.
  Time for first meeting at starting pt = LCM of (L/4, L/1) = L.
  Time for 5th meeting = 5*L/3.
  Time for 17th meeting = 17*L/3.
  
  Both tyms, they meet at pt L/3.
  So, n=4 is valid.
  
  When n = 6 :
  a=6, b=1.
  No:of meeting pts = (6-1)=5pts.
  Meeting pts are : L/5, L/4, L/3, L/2, L .
  Time for first meeting = L/5.
  Time for first meeting at starting pt = LCM of (L/5, L/1) = L.
  Time for 5th meeting = 5*L/5 = L.
  Time for 17th meeting = 17*L/5.
  
  Both tyms, they meet at different pts namely L and L/5.
  So, n=6 is not valid.
• 10 years agoHelpfull: Yes(26) No(1)
• 6
  as the total meeting points(mp) in a circle will be n-1(from ratio of velocities even it is not mentioned,faster will have more velocity=nk)
  
  wnen n=2 mp=1 5th and 17 coincide
  
  when n=6 mp5 5th will coincide with 10th 15th 20th.........
  
  and 17th will coincide with 2th 7th 12th ..............
  
  ans = D) 6
  
• 10 years agoHelpfull: Yes(12) No(6)
• pradeep ...we cant sure for 3 and 4 right ...can u explain some thing clearly
• 10 years agoHelpfull: Yes(2) No(1)
• How do u remember these questions..?? Please submit the and also..
• 10 years agoHelpfull: Yes(1) No(3)
• please explain clearly.....
• 10 years agoHelpfull: Yes(1) No(1)
• plz explain clearly........
• 10 years agoHelpfull: Yes(1) No(1)
• thankss a lot kaustav!!!!
• 10 years agoHelpfull: Yes(1) No(1)
• kaustav how did you determine the meeting points in each case ?
• 9 years agoHelpfull: Yes(1) No(1)
• Meeting points are always equidistant from each other.
• 9 years agoHelpfull: Yes(1) No(1)
• @ KAUSTAV MITRA
  why no. of pts they meet is = a-b ? and why 1st meeting at any of the (a-b) pts = L/(a-b)?
• 9 years agoHelpfull: Yes(1) No(1)
• you are genius
• 8 years agoHelpfull: Yes(1) No(1)
• Check the answer
  http://elitmus-page.blogspot.in/2015/10/a-and-b-started-from-same-point-on.html
• 6 years agoHelpfull: Yes(0) No(0)