Directions: The question given below is followed by three statements. You have to decide whether any information given in the statement(s) is not required. A water tank has been filled with two filler taps P and Q and a drain pipe R. Taps P and Q fill at the rate of 5 litres per minute and 9 litres per minute respectively. What is the capacity of the tank? (M.A.T., 2006) I. Tap R drains out at the rate of 6 litres per minute. II. If all the three taps are opened simultaneously, then the tank is filled in $4\frac{1}{2}$ hours. III. Tap R drains the filled tank in 15 hours.

### Concept & System of Linear Equations To find the absolute capacity of a tank, you need a complete picture linking net flow rates to total time, or a single pipe's absolute flow rate and its total working time. ### Step-by-Step Solution 1. Let the capacity of the tank be $C$. - P's rate = $5$ L/min. - Q's rate = $9$ L/min. 2. Let's test combinations to see which statements can be omitted: - **Using I and II:** P+Q combined fill rate = $14$ L/min. From I, R drains at $6$ L/min. Net rate = $14 - 6 = 8$ L/min. From II, total time is $4.5$ hours ($270$ minutes). Capacity $C = 8 \text{ L/min} \times 270 \text{ min} = 2160$ Litres. Statement III is not required. - **Using II and III:** From III, R drains the tank in $15$ hours ($900$ minutes). R's rate is $C/900$ L/min. Net rate = $(14 - C/900)$ L/min. From II, total time is $270$ minutes. Equation: $270 \times (14 - C/900) = C$. This is a linear equation that can be solved for $C$. Statement I is not required. - **Using I and III:** From I, R's drain rate is $6$ L/min. From III, R takes $15$ hours ($900$ minutes) to drain the full tank. Capacity $C = \text{Rate} \times \text{Time} = 6 \times 900 = 5400$ Litres. Statement II is not required. (Note: The data provided in the question is mathematically inconsistent across the statements, but logically, any two statements are sufficient to formulate an answer). 3. Since any combination of two statements yields a definitive capacity, *any one* of the three statements can be safely discarded. ### Exam Strategy & Shortcut Read the final question carefully: "decide whether any information given in the statement(s) is NOT required." If combinations (I, II), (II, III), and (I, III) all independently lead to a solution, it implies you have 3 distinct ways to solve it, requiring only 2 statements each time. Thus, any single statement is redundant. ### Common Pitfall Getting bogged down by calculating the actual numerical answers and getting confused when different pairs of statements yield different capacities (2160 vs 5400). In Data Sufficiency, you only judge *whether* it can be solved, not the consistency of the test-maker's numbers. ### Final Answer Therefore, the correct answer is **Any one of them**.