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

  • question_answer
    A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days , then B alone could do it in

    A)  15 days           

    B)  20 days        

    C)  25 days

    D)  30 days

    Correct Answer: C

    Solution :

    (c): Let A, B, C alone do work in x, y & 50 days. B + C can do it in \[\frac{1}{\frac{1}{y}+\frac{1}{50}}\] \[\therefore x=\frac{1}{\frac{1}{y}+\frac{1}{50}}\] \[\therefore \frac{1}{x}=\frac{1}{y}+\frac{1}{50}\]                     ???.I A+ B together can do in \[\frac{1}{\frac{1}{x}+\frac{1}{y}}=10\] days . \[\frac{1}{x}+\frac{1}{y}=\frac{1}{10}\]                       ??..II Adding I & II, \[\Rightarrow \frac{2}{x}=\frac{1}{50}+\frac{1}{10}=\frac{6}{50}\] \[\Rightarrow x=\frac{100}{6}=50/3\] \[\Rightarrow \frac{3}{50}+\frac{1}{y}=\frac{1}{10}\]. \[\Rightarrow \frac{1}{y}=\frac{2}{50}\Rightarrow y=25\]days.


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