Best Answer Explained in Below-:

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) * CXNow, simplify the equation:(4/3) * CX + (1/2) * CXTo add these fractions, find a common denominator:(8/6) * CX + (3/6) * CXCombine the fractions:(8/6 + 3/6) * CX(11/6) * CXNow, 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.