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Question 10
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?
Solution
M inlet pipe can fill $$(\frac{M}{8})^{th}$$ part of the tank in 1 hour.
Similarly, N outlet pipes can empty $$(\frac{N}{12})^{th}$$ part of the tank in 1 hour.
=> $$\frac{M}{8} - \frac{N}{12} = \frac{1}{6}$$
=> $$6 M - 4 N = 8$$
=> $$M = \frac{4 + 2 N}{3}$$
If, N = 1, => M = 2 => $$M : N = 2 : 1$$
If, N = 4, => M = 4 => $$M : N = 1 : 1$$
Thus, Ans - (E)
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