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7th Class Mathematics Simple Equations Question Bank Linear Equation in one Variable

  • question_answer
    A mango orchard is split into three blocks A, B & C. In block A, there are n trees, in block B, there are \[\left( n+2 \right)~\]trees an in block C, there are \[\left( n-2 \right)\]trees.
    Block A yields 120 mangoes per tree
    Block B yields 60 mangoes per tree
    Block C yields 180 mangoes per tree
    If the overall average yield per tree is 100 mangoes, find 'n'.

    A)  4   

    B)  3           

    C)  2                                

    D)  1

    Correct Answer: A

    Solution :

    (a) \[\frac{n\times 120+(n+2)60+(n-2)180}{3n}=100\] \[\Rightarrow \,\frac{360n-240}{3n}=100\] \[\Rightarrow 360n-240=300n\] \[\Rightarrow 60n=240\] \[\Rightarrow n=4\] Perfectness of a mathematician A mathematician / Maths student should be able to cross check the correctness of his / her answer in exam hall itself. Since \[n=4,\text{ }\Rightarrow \text{ }n-2=2\] \[\therefore \] Total mangoes \[=\text{ }4\times 120\](Block A) \[+6\times 60\] (Block B) \[+2\times 1850\] (Block C) \[=1200\] Total tress \[=4+6+2=12\] \[\Rightarrow \]Overall average\[=\frac{1200}{12}=100\] Which matches with data in the given question.                 


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