Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 2/3 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what fraction of its capacity?

Let's denote the capacity of drum X as "CX" and the capacity of drum Y as "CY." We're given that drum Y has twice the capacity of drum X, so CY = 2 * CX.

We're also given that drum X is 1/2 full of oil, which means it contains (1/2) of its capacity. Therefore, the amount of oil in drum X is (1/2) * CX.

Drum Y is 2/3 full of oil, which means it contains (2/3) of its capacity. Therefore, the amount of oil in drum Y is (2/3) * CY.

Now, we're pouring all of the oil from drum X into drum Y. So, the amount of oil in drum Y after pouring will be the sum of its original oil content and the oil from drum X:

(2/3) * CY (original oil content in drum Y) + (1/2) * CX (oil from drum X)

Substitute CY = 2 * CX into the equation:

(2/3) * 2 * CX + (1/2) * CX

Now, simplify the equation:

(4/3) * CX + (1/2) * CX

To add these fractions, find a common denominator:

(8/6) * CX + (3/6) * CX

Combine the fractions:

(8/6 + 3/6) * CX

(11/6) * CX

Now, we know that drum Y is filled to (11/6) of its capacity. But we want to express it as a fraction of its capacity, which is CY. Recall that CY = 2 * CX:

So, drum Y is filled to:

(11/6) * CX / (2 * CX)

Simplify by canceling CX:

(11/6) / (2)

Now, simplify further:

(11/6) * (1/2)

Multiply the fractions:

(11/12)

So, drum Y will be filled to 11/12 of its capacity.

The correct answer is 11/12.