Question

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?

Accepted Answer

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

Pipes and Cisterns: Relation between M and N

Explanation

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