four sisters-Suvarna, Tara, Uma and Vihba are playing a game such that the loser doubles the money of each of the other players from her share, They played four games and each sister lost one game in alphabetical order, At the end of fourth game, each sister had Rs.32. How much money did Suvarna start with ?

• Suvarna Tara Uma vihba
  final 32 32 32 32
  fourth 16 16 16 80
  3rd 8 8 72 40
  2nd 4 68 36 20
  1st 66 34 18 10
  so suvarna starts with 66 rupees.
• 10 years agoHelpfull: Yes(5) No(3)
• At the end of fourth game every one had
  Rs.
  32.
  Rs. 32.
  Total money with all the four sisters
  =
  4
  ×
  32
  =
  Rs.
  128
  =4×32=Rs. 128
  
  Total money remains constant because money is only getting transferred among the
  4
  4 sisters. Therefore total money is always
  Rs.
  128
  Rs. 128
  
  Let Suvarna start with
  Rs.
  x
  Rs. x
  Then the total money with the other
  3
  3 sisters
  =
  Rs.
  (
  128
  −
  x
  )
  =Rs. (128−x)
  
  Suvarna lost the first game. She had to give a total of
  Rs.
  (
  128
  −
  x
  )
  Rs. (128−x) to the other
  3
  3 sisters.
  
  Therefore, after the
  1
  1st game, money that Suvarna has
  =
  x
  −
  (
  128
  −
  x
  )
  =
  2
  x
  −
  128
  =x−(128−x)=2x−128
  Total money with the other
  3
  3 sisters
  =
  2
  (
  128
  −
  x
  )
  =2(128−x)
  
  In the second, third and fourth games, other
  3
  3 sisters will lose and each time, Suvarn's money will double.
  
  i.e., after
  2
  2nd game, Suvarn's money
  =
  2
  (
  2
  x
  −
  128
  )
  =2(2x−128)
  i.e., after
  3
  3rd game, Suvarn's money
  =
  4
  (
  2
  x
  −
  128
  )
  =4(2x−128)
  i.e., after
  4
  4th game, Suvarn's money
  =
  8
  (
  2
  x
  −
  128
  )
  =8(2x−128)
  
  8
  (
  2
  x
  −
  128
  )
  =
  32
  2
  x
  −
  128
  =
  4
  2
  x
  =
  132
  x
  =
  66
  8(2x−128)=322x−128=42x=132x=66
  
  Suvarna started with
  Rs.
  66
  Rs. 66
• 6 years agoHelpfull: Yes(0) No(1)