Latest CAT Aptitude Question SOLUTION: 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 sist

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(#M40021722) CAT Logical Reasoning question Keep an EYE

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 ?

Asked In CAT chandreyee chowdhury (10 years ago)

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raghuram dharmavarpu  (10 years ago)

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.

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Anupam Patra  (6 years ago)

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

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