10th Class Mathematics Solved Paper - Mathematics-2016 Outside Delhi Set-I

  • question_answer A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.

    Answer:

    Let the speed of the stream be x km/hr.
    Then speed upstream \[=(24-x)km/hr.\]
    and speed downstream \[=(24+x)km/hr.\]
    Time taken to cover 32 km upstream \[=\frac{32}{24-x}hrs.\]
    Time taken to cover 32 km downstream \[=\frac{32}{24+x}hrs.\]
    \[\therefore \] Time difference \[=\frac{32}{24-x}-\frac{32}{24+x}=1\]
    \[32[(24+x)-(24-x)]=(24-x)(24+x)\]
    \[32(24+x-24+x)=576-{{x}^{2}}\]
                \[64x=576-{{x}^{2}}\]
    \[{{x}^{2}}+64x-576=0\]
    \[{{x}^{2}}+72x-8x-576=0\]
    \[x(x+72)-8(x+72)=0\]
                \[(x+72)(x-8)=0\]
                            \[x=8\] or \[-72\]
    \[\therefore x=8\] (As speed can?t be negative)
    \[\therefore \] Speed of the stream is \[8\,km/h.\]


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