Three boys A, B and C start running at constant speeds from the same point P along the circumference of a circular track. The speeds of A, B and C are in the ratio 5:1:1. A and B run clockwise while C runs in the anticlockwise direction. Each time A meets B or C on the track he gives them a card. What is the difference in the number of cards received by B and C if A distributes 33 cards in all?Please explain the approach

1) 3
2) 7
3) 5
4) 11

• A: B : C = 5:1:1 ===> A & B meet at 4 distinct points ;
  A & C will meet at 6 distinct points.
  When a complete 5 round b& c will complete 1 round
  => a meets b 4 times & a meets c 6 times ( one cycle is completed).
  So at the end of 3 cycle A meets B 12 times & with C 18 times.
  Now in his 16th round A will meet with C but not with B ( as a& b are travelling in same direction so a will be ahead of b) and in his 17th round he meet B & C once.
  So for b = 12+1 = 13 & for c = 18+2 = 20 ;
  So difference = 20-13=7.
• 6 years agoHelpfull: Yes(0) No(0)