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?
Explanation:
Let the total capacity of the tank be 24 units.
∴ The work done by an inlet pipe = 24/8 = 3 units/hour and Work done by an outlet pipe = 24/12 = 2 units/hour
Now, work done by M inlet and N outlet pipes in an hour = 3M – 2N
It taken 6 hours for these pipes to fill the tank completely.
∴ 6(3M – 2N) = 24
∴ 3M – 2N = 4
Now when N = 1, M = 2.
Also when N = 4, M = 4
Similarly we get infinite values of N for which we get different values of M and the ratio M : N cannot be determined uniquely.
Hence, option (e).
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