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)