Explanation: Let \(C\) be the maximum capacity of the tank. Half full is \(C/2\). When \(30\) liters is added, the total amount of water is \(C/2 + 30\). The amount of water in the tank **increases by** \(1/3\). This phrase is ambiguous. Option 1: The increase is \(1/3\) of the *current* amount (\(C/2\)). The increase is \(30\) liters. So, \(30 = 1/3 \times (C/2) \Rightarrow 30 = C/6 \Rightarrow C = 180\) liters. Option 2: The increase is \(1/3\) of the *capacity* (\(C\)). The increase is \(30\) liters. So, \(30 = C/3 \Rightarrow C = 90\) liters. The problem states "the amount of water in the tank increases by 1/3." The logical interpretation in these types of problems is usually based on the existing amount (Option 1). However, the given explanation implies the result is 180: "This means 1/3 of half of the tank is 30 liters. So half of the tank is 90 liters. So the maximum water holding capacity of the tank is 180 liters." Since 180 is not an option, and the provided explanation gives 180 as the answer, the correct option must be "None of these" (5).
