Rahul took part in a cycling game with many others in a circular closed circuit. After pedaling for several minutes, he found that 1/5th of the cyclists ahead of him and 5/6th of the cyclists behind him together formed the total no. of participants. How many were participating in the race?

• In the circle, the no. of cyclists ahead of Rahul = no. of cyclists behind him. And let the no. of participants in the race excluding Rahul be x.
  so the total no. of participants in the race=x+1.
  A/Q, x/5 + 5x/6 = x+1
  On solving, we get x=30.
  hence, the total no. of participants in the race= x+1= 30+1=31
  Ans.=31.
• 13 years agoHelpfull: Yes(23) No(4)
• 30.
  1/5 th are ahead,5/6th are behind and one himself(rahul).Now assume total no of participants to be x.
  thus, x = (x/5)+(5x/6)+1
  x/30=1
  x=30.
• 13 years agoHelpfull: Yes(7) No(15)
• let the number of participants be x.
  
  then x/5 + 5x/6 + 1 = x (including rahul)
  
  solvng we get 30.
  
  u can get a doubt like, 1/5th of 30 is 6 and 5/6th of 30 is 25, when u sum all the three, 25+6+1 = 32.. but we got 30.
  as it is a circle, the cyclist who is leading rahul, can also be behind him. if the track is a straight path, then this ans is not correct :-)
• 13 years agoHelpfull: Yes(4) No(2)
• 1/5(x-1)+5/6(x-1)=x
  x=31.
• 10 years agoHelpfull: Yes(3) No(0)
• the solution to this problem can be given this way->
  on a closed circuit say n participants are cycling.
  except Rahul there are n-1 participants
  therefore according to Rahul following linear equation can be framed->
  1/5(n-1) + 5/6(n-1) = n
• 11 years agoHelpfull: Yes(2) No(0)
• dera friends 1/5 th of 30 is 6
  and 5/6 th of 30 is 25
  so including rahul the total no. of cyclist as per u r answer would be 32
  u r answer would not satisfy the equation
• 13 years agoHelpfull: Yes(1) No(2)
• 30...let total no of particiants be x derefore d equation becomes x=x/5+5x/6+1.
• 13 years agoHelpfull: Yes(1) No(1)
• 1/5(x-1)+5/6(x-1)=x
  =>31
• 10 years agoHelpfull: Yes(1) No(0)
• for rahul total no. of cyclist would be one less than total no. of participants
  thus
  the equation formed would be like this
  
  x/5+5x/6=x-1
  
  on solving this the sol is
  30
• 13 years agoHelpfull: Yes(0) No(4)
• LCM of 5 & 6=30
  After taking LCM, (1/5)+(5/6)=(6+25)/30=31/30
  where numerator>denominator because we have included Rahul whereas 1/5 & 5/6 represents the other cyclists.
  Hence answer is 31.
• 7 years agoHelpfull: Yes(0) No(0)
• let the total number = x
  since it is a closed circle = x-1
  now,
  
  (1/5+5/6)(x-1)=x
  =>(31/30)(x-1)=x
  =>(31/30)x-31/30=x
  =>(1/30)x=31/30
  
  therefore the number of people participating in the race is 31
• 6 years agoHelpfull: Yes(0) No(0)