Xavier Aptitude Test 2016 Paper

Question : 64 of 103

Marks: +1, -0

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?

M : N = 1 : 1
M : N = 2 : 1
M : N = 2 : 3
M : N = 3 : 2
None of the above

Validate

Solution:

(e) Mintel pipes can fill the

\ (\ {\ {M}}/{8} )^{ { th }}

Part of the tank in 1 hour
Similarly

{N}

outlet pipes can empty

(\ { {N}}/{12}\r )^{\ {th}}

part of the tank in 1 hour

∴\ {{\ N}}/{8}- {\ {N}}/{12}= {1}{6}

6M – 4N = 8

{M}= {4+2 \ {N}}/{3}

...........(1)
So there will be infinite number of solutions (N = 1, 4, 7, --)
but none of the ratios given in the option are correct.
forere – When M = 2, N = 1 or M = 4, N = 4
eq (1) can be solved.
But when M = 4, N = 2 or M = 2, N = 2
Solution of eq (1) doesn't satify.

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