Different letters represent different digits and none of the letters i

This is quite an interesting question where figuring out a logical first step might not be straightforward, or at least it wasn't for me. And coming up with all the right algebraic equations within 2 mins might look like a daunting task.

But with intuition and right kind of strategy, it beautifully unravels itself.

As all the digits are single digit numbers, my few initial takeaways from the equation were -

I + 1 = L
L + I + 1/2 = I => L + 1/2 = 10

The first equation although small gives us a good hint, that both L and I are consecutive numbers. And from second we can say that these numbers are on the higher end of the spectrum, so my next logical step would be to assume these 2 numbers to be either 8/9 or 7/8

Now either I can try both of these sequentially and see if I am able to crack the value of A, or a better one would be to check the options and see if we have a multiple of either 8*9 = 72 or 7*8 = 56

There's only one option which seems valid => 144 => 72*2 ie. A = 2, I = 8, L = 9

Let's quickly right down the numbers and verify the answer,

xx2
x99
888
----
989

Bingo!

IMO: E