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SSC Sample Paper SSC-CGL TIER - I Sample Test Paper-4

  • question_answer
    On walking along the diagonal of a rectangular ground at the speed of 52 metre/min, A takes 15 seconds to cross  the ground while walking along the sides at the speed of 68 m/min, B takes the same time to cross the ground. Area of the field (in \[{{m}^{2}}\]) is -

    A) 30                                

    B) 40

    C) 50                                

    D) 60

    Correct Answer: D

    Solution :

    Length of diagonal = \[52\times \frac{15}{60}=1\] Length along sides =                     \[68\times \frac{15}{60}=17m\] Now, l + b = 17 and \[\sqrt{{{l}^{2}}+{{b}^{2}}}\]= 13 \[\begin{align} & \Rightarrow \,\,\,\,\,\,\,\,\,\sqrt{{{l}^{2}}+{{b}^{2}}}=169 \\ & \Rightarrow \,\,\,\,\,\,\,\,\,{{(17-b)}^{2}}+{{b}^{2}}=169 \\ \end{align}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,289-34b+2{{b}^{2}}=169\] \[\begin{align} & \Rightarrow \,\,\,\,\,\,\,\,\,{{b}^{2}}-17b+60=0 \\ & \Rightarrow \,\,\,\,\,\,\,\,\,(b-12)\left( b-5 \right)=0 \\ & \Rightarrow \,\,\,\,\,\,\,\,\,b=5,12\Rightarrow l=12,5 \\ \end{align}\] \[\therefore \] Area of the ground =12 x 5= 60m2


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