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

  • question_answer
    A and B undertake to do a piece of work for Rs. 600. A alone can do it in 6 days while B alone can do it in 8 days but with the help of C, they finish it in 3 days. Find the share of C.

    A)  Rs. 75  

    B)  Rs. 90          

    C)  Rs. 110                        

    D)  Rs. 85

    Correct Answer: A

    Solution :

    (a): A, B, C can do (alone) work in 6 days, 8 days, & x days (assume) respectively. \[\therefore \] Together, they will do it in \[\frac{1}{\frac{1}{6}+\frac{1}{8}+\frac{1}{x}}\]=days. Now, \[\frac{1}{\frac{1}{6}+\frac{1}{8}+\frac{1}{x}}=3\] \[\Rightarrow \frac{1}{6}+\frac{1}{8}+\frac{1}{x}=\frac{1}{3}\]. \[\Rightarrow \frac{1}{x}=\frac{1}{3}-\frac{1}{6}-\frac{1}{8}=\frac{1}{24}\Rightarrow x=24\]days. Efficiency ratio of A : B : C \[=\frac{1}{6}:\frac{1}{8}:\frac{1}{24}=4:3:1\] Share of C \[=\frac{1}{4+3+1}\times 600=Rs75/-\]         


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