A and B run in opposite directions from a pt. P on a circle with different but constant speeds. A runs in clockwise direction. They meet for the first time at a distance of 900 m in clockwise direction from P and for the second time at a distance of 800 m in anticlockwise direction from P. If B is yet to complete one round, the circumference of the circle is

a) 1700m b) 1250m c) 1300m d) 1200m

• 1300 answer
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• p is the perimeter of the circle
  Suppose after t1 time they first met and a is the speed of A and b is the speed of B
  
  
  a*t1=900
  b*t1=-p+900 {p is minus for anti clock wise direction}
  
  
  Suppose after time t2 they again met
  
  b*t2=-800
  a*t2= p+p -800 {extra p because the A is on its second round}
  
  
  so from first set of equation
  
  we have
  
  a/b=900/(-p+900)
  
  and from second set we have
  a/b= (2p-800)/-800
  
  so from these two equation compare their R.H.S
  
  we have (2p-800)/-800 = 900/(-p+900)
  
  
  cross multiply
  
  then we have
  
  -2psquare + 1800 p +800p = 0
  
  simplify the equation we have
  
  
  psquare - 1300p=0
  
  finally we have p= 1300
  
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