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8th Class Mathematics Direct and Inverse Proportions Question Bank Direct & Inverse Proportional (Time & Work)

  • question_answer
    Two pipes can fill a cistern in 14 hours and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom it took 32 min. more to fill the cistern. When the cistern is full, in what time will the leak empty it?

    A)  100 hours        

    B)  111 hours

    C)  112 hours  

    D)  114 hours

    Correct Answer: C

    Solution :

    (c): Let leakage take 'x' hrs to empty. Let 't' be time, had there been no leakage. \[\therefore \frac{1}{t}=\frac{1}{14}+\frac{1}{16}\Rightarrow t=\frac{224}{30}\] Also. \[\left( t+\frac{32}{60} \right)hrs=\frac{1}{\frac{1}{14}+\frac{1}{16}-\frac{1}{x}}\] \[\Rightarrow \frac{224}{30}+\frac{8}{15}=\frac{1}{\frac{1}{14}+\frac{1}{16}-\frac{1}{x}}\] \[\Rightarrow 8=\frac{1}{\frac{1}{14}+\frac{1}{16}-\frac{1}{x}}\Rightarrow \frac{1}{x}=\frac{1}{14}+\frac{1}{16}-\frac{1}{8}=\frac{1}{14}-\frac{1}{16}\] \[\Rightarrow \frac{1}{x}=\frac{2}{14\times 16}\Rightarrow x=112\]hrs


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