SATHEE: Quantitative Aptitude Ques 2220

Quantitative Aptitude Ques 2220

Question: Two pipes A and B can fill a tank in 24 and 32 min, respectively. If both the pipes are opened together, after how much time pipe B should be closed, so that the tank is full in 9 min?

Options:

A) 40 min

B) 30 min

C) 10 min

D) 20 min

Show Answer

Answer:

Correct Answer: D

Solution:

Part filled by A in 1 min $ =\frac{1}{24} $ Part filled by B in 1 min $ =\frac{1}{32} $ Let B is closed after x min. Then, [part filled by $ (A+B) $ in x min] + [part filled by A in $ (9-x) $ min] = 1

$ \therefore $ $ x( \frac{1}{24}+\frac{1}{32} )+(9-x)\times \frac{1}{24}=1 $

$ \Rightarrow $ $ x( \frac{4+3}{96} )+\frac{(9-x)}{24}=1 $

$ \Rightarrow $ $ \frac{7x}{96}+\frac{(9-x)}{24}=1 $
$ \Rightarrow $ $ \frac{7x+4(9-x)}{96}=1 $

$ \Rightarrow $ $ 7x+4(9-x)=96 $
$ \Rightarrow $ $ 7x+36-4x=96 $

$ \Rightarrow $ $ 7x-4x=96-36 $
$ \Rightarrow $ $ 3x=60 $
$ \Rightarrow $ $ x=\frac{60}{3}=20 $ Hence, B must be closed after 20 min.

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