Quantitative Aptitude Ques 1023

Question: Two pipes P and Q can fill a cistern in 12 and 15 min, respectively. If both are opened together and at the end of 3 min, the first is closed. How much longer will the cistern take to fill?

Options:

A) $ 8\frac{1}{4}\min $

B) $ 8\frac{3}{4}\min $

C) $ 5\min $

D) $ 8\frac{1}{2}\min $

Show Answer

Answer:

Correct Answer: A

Solution:

  • Given, time taken by P to fill the tank =12 min and time taken by Q to fill the tank = 15 min Then, pan filled by both pipes in 1 min $ =\frac{1}{12}+\frac{1}{15}=\frac{5+4}{60}=\frac{9}{60} $ Now, part filled in 3 min $ =\frac{3\times 9}{60}=\frac{27}{60}=\frac{9}{20} $

$ \therefore $ Remaining part $ =1-\frac{9}{20}=\frac{11}{20} $ Now, the remaining part is filled by pipe Q in x min.

$ \therefore $ Remaining time = Remaining part $ \times $ Q’s time

$ \Rightarrow $ $ x=\frac{11}{20}\times 15=\frac{11\times 3}{4}=\frac{33}{4}=8\frac{1}{4}\min $

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