Lets try to design the possible number line first.

Tips:-
* keep A as constant.
* Mark C as C1 and C2 on the both sides of A. (C1 and C2 could be the possible location of C)
* Mark B as B1, B2, B3 and B4 where

B1 is extreme left to A, C1 and C2
B2 lies between C1 and A
B3 lies between A and C2
B4 lies extreme right to A, C1 and C2

Assumption: None of the point overlap each other.

So our number line would like something like this:-

------B1------C1------B2------A------B3------C2------B4------

Now by condition 1:

B = A + 3
This will rule out B1 and B2 from the above number line. So, our new number line would be something like this:-

-----------C1--------------A------B3------C2------B4------

B = C - 5
This will rule out C1 and B4 from the above number line. So, our new number line would be something like this:-

---------------------------A------B3------C2--------------

B lies between A and C. hence condition 1 is SUFFICIENT.

Condition 2:

Again draw the number line:

------B1------C1------B2------A------B3------C2------B4------

C = A + 8
This will rule out C1 from the above number line. So, our new number line would be something like this:-

------B1--------------B2------A------B3------C2------B4------

again C = B + 5, it means B <C> A
therefore, This will rule out B1, B2, and B4 from the above number line. So, our new number line would be something like this:-

---------------------------A------B3------C2--------------

B lies between A and C, hence condition 2 is also alone SUFFICIENT.

Better yet assume a number for C=10

(1) b=5 and a=2
(2) b=5 and a=2


so both sufficient.

D is ans here.

From q itself : is a<b<c>a
b=c-5 so b< c sufficient

From 2: c=5+b so b<c> a and also, b>a since 3 is added with 5+a.
Sufficient.