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Here X1 is represented in Binary and X2 in Hexadecimal.

taking X1 : (23.6)10 -----> 23 can be easily converted to binary as = (10111)2

now for decimal values... 

1)multiply mantissa by 2

2)record the characteristics and remove from the new value.

3)repeat step 1 and 2 until mantissa is 0. or as per your need.

  for .6 

1).6*2 = 1.2

2) characteristic(c1) =1 mantissa(m1) = .2

simlarly we will get c2=0 M2=.4  ::   c3=0 m2=.8  ::  c4=1 m4=.6 :: c5=1 m5=.2 . so value becomes (10111.1001100110011....)

X1 is recurring value 0011 .

now for X2=(65.535)10

65 can be easily represented as (41)16 now for mantissa repeat the above steps but instead of 2 multiply mantissa by 16(for hexadecimal)

m1=8 c1=.56 :: m2=8 c2=.96 :: m3=15(F) c3=.36  ::  m4=5  c4=.76  :: m5=12(C) c5=.16 :: m6= 2 c6= .56 :: m7= 8 c7= .96

so X2= (41.88F5C28F5C28.....)16

X2 is recurring value F5C28

so it matches with option D.

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X1 is not matching with option B and neither X2  ans may be D
@sanjay sir can u check now i updated... I forgot to calculate further for X2

@Sanjay Sharma

sir, you ask in the question faster method.... therefore you have some other procedure.

what is that procedure?

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