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Pipes and Cisterns: Relation between M and N

XAT 2016 · Quantitative Ability & Data Interpretation · Medium · Quantitative Ability

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A water tank has M inlet pipes and N outlet pipes. An inlet pipe can fill the tank in 8 hours while an outlet pipe can empty the full tank in 12 hours. If all pipes are left open simultaneously, it takes 6 hours to fill the empty tank. What is the relationship between M and N?

  1. A.

    M : N = 1 : 1

  2. B.

    M : N = 2 : 1

  3. C.

    M : N = 2 : 3

  4. D.

    M : N = 3 : 2

  5. E.

    Cannot be determined.

Answer

E

Explanation

Rate equation per hour: M8−N12=16\frac{M}{8} - \frac{N}{12} = \frac{1}{6} Multiply by 24: 3M−2N=43M - 2N = 4 Since there are multiple integer solutions for (M,N)(M, N) (e.g., M=2,N=1  ⟹  M:N=2:1M=2, N=1 \implies M:N = 2:1; M=4,N=4  ⟹  M:N=1:1M=4, N=4 \implies M:N = 1:1), the unique ratio M:NM:N cannot be determined.

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