8th Class Mathematics Direct and Inverse Proportions Question Bank Direct and Inverse Proportions

  • question_answer A cistern has two inlets A and B which .can fill it in 12 minutes and 15 minutes respectively. An outlet C can empty the full cistern in 10 minutes. If all the three pipes then are opened together in the empty cistern, time taken to fill the cistern completely is _____.

    A)  20 minutes                 

    B)         10 minutes     

    C)         15 minutes                 

    D)         5 minutes       

    Correct Answer: A

    Solution :

    Part of cistern filled by inlets A and B together in one minute \[=\frac{1}{12}+\frac{1}{15}=\frac{5+4}{60}=\frac{9}{60}\] and part of cistern emptied by outlet C in 1 minute \[=\frac{1}{10}\] So, part of the cistern filled in one minute when all three pipes are opened simultaneously, \[=\frac{9}{60}-\frac{1}{10}=\frac{9-6}{60}=\frac{3}{60}=\frac{1}{20}\] So, time required to fill the cistern = 20 mins.


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