A hare and a tortoise have a race along a circle of 100 yard diameter. The tortoise goes in one direction and the hare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hare increase its speed so as to tie the race?
a) 37.80
b) 5
c) 40
d) 8

• 37.8
  
  Hare starts after tortoise covers 1/5th distance .
  When hare covers 1/8th of distance tortoise meets hare
  So distance covered by tortoise = 1-(1/5 + 1/8)
  = 27/40
  Time taken by both is same
  time = dist/speed
  So (dist/ speed) of tortoise = (dist / speed) of hare
  let speed of tortoise be t and of hare be h
  27/40t = 1/8h
  h = (40/(8*27) )* t = 5/27 * t
  Now for the next part hare has to cover 7/8 th distance when tortoise covers 1/8 th distance
  so we get
  1/8t = 7/8h
  h = 7t
  so the factor by which h's speed increases = 7t/ (5/27 * t)
  = 37.8
• 13 years agoHelpfull: Yes(221) No(10)
• let total distance to cover=x
  nw first tortoise goes x/5
  after dat when they meet together,
  hare goes x/8
  and so tortoise goes x-(x/5+x/8)=27x/40
  so, ratio of tortoise and hare=27x/40 : x/8=27:5
  nw to tie up the incresed fctor of spped of hare be v
  then,
  
  (x/8)/27=(x-x/8)/5v
  or, 1/27=7/5v
  or, v=(27*7)/5=37.80
  
  option (c) is correct
  
• 12 years agoHelpfull: Yes(17) No(5)
• 37.8
• 13 years agoHelpfull: Yes(13) No(12)
• for getting answer quickly....
  first distance = 1/x
  second distance = 1/y
  
  let z = xy-x
  required factor will be = z*(z-y)/x^2
  
  in this question..
  x=5 , y=8
  z=5*8-5=35
  z-y = 35-8 = 27
  required factor = 35*27/25 = 37.8 ans
• 11 years agoHelpfull: Yes(8) No(4)
• It is 37.80
• 13 years agoHelpfull: Yes(5) No(13)
• Ans:37.8
• 13 years agoHelpfull: Yes(5) No(10)
• (remember the following 4 steps for these type of qstn.)
  1/5 1/8
  1)5*8=40
  2)40-5=35
  3)35-8=27
  4)(27*35)/5^2=37.8
  
• 9 years agoHelpfull: Yes(5) No(1)
• expalin dis plzz.me unable 2 get d logic..
  
• 11 years agoHelpfull: Yes(4) No(0)
• Ans: a
  
  
• 13 years agoHelpfull: Yes(2) No(14)
• 40
• 13 years agoHelpfull: Yes(2) No(33)