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      Question

      Pipe 'X' can fill a tank in 24

      hours. Pipe 'Y' can fill the same tank in 36 hours. If pipe 'X' is started ___ hours after pipe 'Y', then the tank will be completely full in __ hours after pipe 'X' was first opened. The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true? I. 8, 11.2 II. 11, 10 III. 15, 8.4
      A Only I Correct Answer Incorrect Answer
      B Only I and III Correct Answer Incorrect Answer
      C Only II Correct Answer Incorrect Answer
      D Only I and II Correct Answer Incorrect Answer
      E All of I, II and III Correct Answer Incorrect Answer

      Solution

      ATQ, Let the capacity of the tank be 72 litres. So, efficiency of pipe 'X' = (72/24) = 3 litres/hour And efficiency of pipe 'Y' = (72/36) = 2 litres/hour For I: Tank filled by pipe 'Y' in 8 hours = 2 X 8 = 16 litres And remaining capacity of the tank = 72 - 16 = 56 litres So, time taken by both pipes to fill the tank = 56 ÷ (3 + 2) = 11.2 hours So, statement I is true. For II: Tank filled by pipe 'Y' in 11 hours = 2 X 11 = 22 litres And remaining capacity of the tank = 72 - 22 = 50 litres So, time taken by both pipes to fill the tank = 50 ÷ (3 + 2) = 10 hours So, statement II is true. For III: Tank filled by pipe 'Y' in 15 hours = 2 X 15 = 30 litres And remaining capacity of the tank = 72 - 30 = 42 litres So, time taken by both pipes to fill the tank = 42 ÷ (3 + 2) = 8.4 hours So, statement III is true.

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