8th Class Mathematics Sample Paper Mathematics Sample Paper - 3

  • question_answer
    (a) Divide 34 into two parts in such a way that \[{{\left( \frac{4}{7} \right)}^{th}}\]of one part is equal to \[{{\left( \frac{2}{5} \right)}^{th}}\]of the other.
    (b) Which of the following equation are linear equation in one variable.
    (a) \[{{x}^{2}}+x=1\]                   
    (b) \[2x-7=\frac{2}{3}\]
    (c) \[{{x}^{2}}+\text{ }x=10~\]                     
    (d) \[x-15=3x\]


    (a)  Let,             Ist part = x
    Then, IInd part \[=\left( 34\text{ }-\text{ }x \right)~\]                                                                                                                    
    According to question,
    \[{{\left( \frac{4}{7} \right)}^{th}}\] of Ist part \[{{\left( \frac{2}{5} \right)}^{th}}\]  of IInd part                                                                                                                                                    
    or             \[\frac{4}{7}x=\frac{2}{5}(34-x)\]
    or             \[20x\text{ }=\text{ }14\left( 34-x \right),\]         
    [by cross multiplication]
    or         \[~20x\text{ }=\text{ }14\text{ }x\text{ }34\text{ }-\text{ }14x\]             
    or             \[20x+14x=14\times 34\]
    or                        \[34x=14\times 34\]
    or         \[x=\frac{14\times 34}{34}\]                                                                                                                              
    or                     x=14
    Hence, two parts are 14 and \[34\text{ }-14\text{ }=\text{ }20\]
    i.e.,                    1st part = 14 and Und part = 20
    (b) Linear equation in one variable are
    (c) \[2x-7=\frac{2}{3}\]and(d) \[x-15=3x\]          


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