A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after the tortoise has covered 1/3 of its distance and that too leisurely. The hare and tortoise meet when the hare has covered only 1/4 of the distance. By what factor should hare increase its speed so as the win the race?
(a) 4
(b) 3
(c) 12
(d) 5

• The circle circumference is given by the formula 2*pi*r or(pi x diameter) = 100pi yards.Therefore this is the length of the race.
  
  The tortoise has a 100pi/ 3 = 33.33 pi head start
  The hare sets off leisurely and gets 1/4 of the way round ie 1/4 x 100 pi= 25 pi yards when he meets the tortoise
  therefore by d time hare move 25 pi ,the tortoise move (100-33.33-25)=41.66pi yards
  Therefore just to go at the same speed as the tortoise, the hare must increase his speed by a factor of 41.66/25 = 1.664
  now the tortoise only has 25pi yards to the finish, while the hare has 75pi yards to go. hence hare must increase his speed by a factor of 75/25 = 3 to allow for larger distance to go
  hence to tie d race he mst increase his speed by a factor of
  1.664*3 = 4.992 approx (5)
• 12 years agoHelpfull: Yes(12) No(3)
• 1/3,1/4
  3*4=12
  12-3=9
  9-4=5
  9*5/3*3=45/9=5.00
  ans is d.
• 12 years agoHelpfull: Yes(8) No(6)
• 100pie.......1/8(100)::12.5..100-12.5...87.5,....87.5-20:::67.5.......compare the speed.....ans is 5
• 9 years agoHelpfull: Yes(0) No(0)