Directions: Each of the questions below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question: A tank is fitted with two taps A and B. In how much time will the tank be full if both the taps are opened together? (SNAP, 2005) I. A is 50% more efficient than B. II. A alone takes 16 hours to fill the tank. III. B alone takes 24 hours to fill the tank.

### Concept & Efficiency and Time Relationship To find the combined time required for two taps to fill a tank, we need their individual times or their individual rates. Efficiency and time are inversely proportional. ### Step-by-Step Solution 1. We need to find the combined time of A and B. This requires knowing the individual times for both A and B, or knowing one time and the ratio of their efficiencies. 2. Let's evaluate the combinations: - **From I and II:** Statement I gives the efficiency ratio (A is 150% of B, so Time of A : Time of B = 2 : 3). Statement II gives A's time as 16 hours. We can calculate B's time ($16 \times 1.5 = 24$ hours) and then find the combined time. (Sufficient) - **From I and III:** Statement I gives the efficiency ratio. Statement III gives B's time as 24 hours. We can calculate A's time ($24 \times (2/3) = 16$ hours) and then find the combined time. (Sufficient) - **From II and III:** Statement II gives A's time (16 hours) and Statement III gives B's time (24 hours). We can directly find the combined time using the formula $\frac{xy}{x+y}$. (Sufficient) 3. Since any pair of the statements provides enough information to solve the problem, any two of the three statements are sufficient. ### Exam Strategy & Shortcut When you have three variables (Time A, Time B, and their Ratio) and an equation linking them, knowing any two allows you to find the third. In Data Sufficiency, once you spot this relationship, you can immediately conclude that any two statements will work without doing the actual arithmetic. ### Common Pitfall Choosing "II and III only" because they provide direct numbers, while failing to realize that Statement I provides the mathematical bridge needed to use just one of the absolute values. ### Final Answer Therefore, the correct answer is **Any two of the three**.