Multiple choice

The question below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer. Find the respective ratio of the efficiencies of pipe P and pipe Q. Statement I: Pipe P and pipe R together can fill the tank in 48 minutes. With pipe Q, they can fill the tank in 80/3 minutes. Statement II: Pipe Q and pipe R with double of their efficiency can fill the tank in 120/7 minutes. Statement III: Pipe P and pipe Q together can fill the tank in 40 minutes. Respective ratio of the efficiencies of pipe P and pipe R is 2:3.

  1. Only II and III

  2. Only I and either II or III

  3. Any two of the three

  4. All I, II and III

  5. Cannot be answered even after combining all the statements.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I: (1/P + 1/R) = 1/48 and (1/P + 1/Q + 1/R) = 3/80. Subtracting gives 1/Q = 3/80 - 1/48 = 1/120, so Q = 120 minutes. Statement II: With Q and R at double efficiency: 2/Q + 2/R = 7/120, giving 1/Q + 1/R = 7/240. Statement III: (1/P + 1/Q) = 1/40 and P:R = 2:3 gives 3P = 2R. Using Statement I and III together gives both P and Q. Using II and III together also works. Any two statements are sufficient.

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