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CAT 1995 | Question: 71

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Four sisters Suvarna, Tara, Uma, and Vibha 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 the alphabetical order. At the end of fourth game each sister had Rs. 32.

What was the amount with Uma at the end of the second round?

  1. 36
  2. 72
  3. 16
  4. None of these

1 Answer

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If we follow backward approach, it can be easy to find the answer. 

 each sister lost one game in the alphabetical order, so in 1st round Suvarna lost, in 2nd round Tara lost, in 3rd round Uma lost & in 4th or last round Vibha lost.                                            

ROUND Suvarna Tara Uma Vibha
4th (Vibha lost) 32 32 32 32
3rd (Uma lost)

32 / 2

=16

32 / 2

=16

32 / 2

=16

32+16+16+16

=80
2nd (Tara lost)

16 / 2

=8

16 / 2

=8

16+40+8+8

=72

80 / 2

=40
1st (Suvarna lost)

8 / 2

=4

8+4+36+20

=68

72 / 2

=36

 40 / 2

=20
Initial

4+34+18+10

=66

68 /2

=34

36 /2

=18

20 /2

=10

 

Therefore, at the end of 2nd round, Uma has 72 rupees.(B)

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