Quantitative Aptitude Ques 1737

Question: A pipe P can fill a tank in 12 min and another pipe R can fill it in 15 min. But, the 3rd pipe M can empty it in 6 min. The 1st two pipes P and R are kept open for double the 2.5 min in the beginning and then the 3rd pipe is also opened. In what time is the tank emptied?

Options:

A) 30 min

B) 25 min

C) 45 min

D) 35 min

E) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

  • According to the question, Double the $ 2.5\min =5\min $ Now, part filled in 5 min $ =5\times ( \frac{1}{12}+\frac{1}{15} ) $ $ =5\times ( \frac{5+4}{60} )=5\times \frac{9}{60}=\frac{3}{4} $ Part emptied in 1 min when P, R and M, all are opened. $ =\frac{1}{6}-( \frac{1}{12}+\frac{1}{15} )=\frac{1}{6}-( \frac{5+4}{60} )=( \frac{1}{6}-\frac{3}{20} )=\frac{1}{60} $ One-sixtieth part is emptied in 1 min.

$ \therefore $ Three-fourth part will be emptied in $ 60\times \frac{3}{4}=15\times 3=45\min $

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