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SSC Sample Paper SSC CGL - Sample Paper-4

  • question_answer
    Two pipes A and B can separately fill a cistern in 60 min and 75 min respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 min. In how much time third pipe alone can empty the cistern?

    A)  110 min                       

    B)  100 min

    C)  120 min                       

    D)  90 min

    Correct Answer: B

    Solution :

    Let the third pipe can empty the cistern in x min. Part of cistern filled in 1 min when all three pipes are opened simultaneously \[=\frac{1}{60}+\frac{1}{75}-\frac{1}{x}\] According to the question, \[=\frac{1}{60}+\frac{1}{75}-\frac{1}{x}=\frac{1}{50}\] \[\Rightarrow \]   \[\frac{1}{x}=\frac{1}{60}+\frac{1}{75}-\frac{1}{50}\]             \[=\frac{5+4-6}{300}=\frac{3}{300}\] \[\Rightarrow \]   \[=\frac{1}{x}=\frac{3}{300}\] \[\therefore \]      \[x=\frac{300}{3}=100\,\min \]


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