Question 59

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)

Create a FREE account and get:

CAT Quant Questions | CAT Quantitative Ability

Tank - Pipes