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: If both the pipes are opened, how many hours will be taken to fill the tank? I. The capacity of the tank is 400 litres. II. The pipe A fills the tank in 4 hours. III. The pipe B fills the tank in 6 hours.

### Concept & Rates of Work The time taken to fill a tank by multiple pipes depends exclusively on their individual times or rates expressed as a fraction of the total tank per unit time. The absolute capacity of the tank in liters is irrelevant for determining the time in hours if individual times are already given. ### Step-by-Step Solution 1. The question asks for the total time to fill the tank when both pipes are open. 2. Statement II gives the time for pipe A alone: 4 hours. Therefore, A's rate is $1/4$ of the tank per hour. 3. Statement III gives the time for pipe B alone: 6 hours. Therefore, B's rate is $1/6$ of the tank per hour. 4. Using II and III, the combined rate is: $$ \frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12} $$ 5. The combined time is the reciprocal of the combined rate, which is $12/5$ hours. We successfully answered the question using only II and III. 6. Statement I provides the tank's capacity (400 litres). Since we only need the time, the total volume is completely unnecessary. ### Exam Strategy & Shortcut Whenever a problem asks for time and provides individual times, any absolute volume or capacity data is extraneous noise designed to confuse you. Ignore it immediately. ### Common Pitfall Thinking that "capacity" is required to find the final time and incorrectly selecting "All I, II and III". Remember that fractional work methods do not require knowing the actual volume. ### Final Answer Therefore, the correct answer is **Only II and III**.