SSC Quantitative Aptitude Pipes & Cisterns Question Bank Pipe and Cistern (II)

A pipe can fill a cistern in 12 min and another pipe can fill it in 15 min, but a third pipe can empty it in 6 min. The first two pipes are kept open for 5 minutes in the beginning and then the third pipe is also opened. Number of minutes taken to empty the cistern is

A) 38

B) 22

C) 42

D) 45

Correct Answer: D

Solution :

[d] Let the number of minutes taken to empty the cistern be x min. According to the question, \[\frac{x}{6}-\frac{x+5}{12}=\frac{x+5}{15}=0\] \[\Rightarrow \] \[\frac{x}{6}-\frac{x}{12}-\frac{x}{15}=\frac{5}{12}+\frac{5}{15}\] \[\Rightarrow \] \[\frac{x}{60}=\frac{45}{60}\] \[\Rightarrow \] \[x=45\min \]

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