Hi Arnab, I hope this
helps.

Let us Assume T = (1.a,
1.b, etc). This consists of 3o decimals.

 Now let’s find out E. In E Tenths digit even
rounded up and tenths digit odd rounded down. 1/3 of the decimals of the
decimals in T whose tenths digit is even. So there are 10 decimals like that.

So say for an example say if
decimal value is 1.2 is rounded to 2. If it is 1.1 it is rounded to 1.

So therefore E = 40 (due to rounding of ten even and 20 odd) .

Since the question is
asking for possible value. Let find out minimum and maximum values.

S max = 30 + 10(.8) +
20(.9) = 56( maximum value for an even and odd in tenths place ) 
S min = 30 + 10(.2) + 20(.1) = 34 ( minimum value for an even and odd in
tenths place ) 

E-S min = 40 – 56 = -16 
E-S max = 40 – 34 = 6 
Thus, the min/max of E is -16 and 6, so I , II apply. 

III statement is beyond
the range.

So answer is C. I and II
only.

Can any one please show me a easy way of solving this question as the solution given in the OG has confused me –

Thank you for the explanation. 

Glad it helped.

@arnab  I suppose II option is 6 ????

yes answer option II  is 6 only. Typo error.