Although best answer contain all information but i want to demonstrate by example lets take one example of 3x3 lower triangular matrix
now above matrix is stored on following basis in new representation
Now to find index of (i,j)th element by assuming that both array representations are starting from 1.
now lets find the location of element (2,2) by all options
A) i+j = 2+2 = 4 (wrong)
B) i+j-1 = 2+2-1 =3 (right) but check for (3,1) and it will give the same answer so (wrong).
C) (j-1) + i(i-1)/2 = 1 + 2.1/2 =2 (wrong)
D) i + j(j-1)/2 = 2 + 2.1/2 =3 (right) check for (3,1) also it will give the same answer so (wrong).
So clearly no option is matching either answer should be j + i(i-1)/2 or if new array representation will start from 0 then answer will be C.