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10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank Linear Equation in two Variables

  • question_answer
    A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time and, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

    A)  75 km                         

    B)  150 km       

    C)  300 km            

    D)  600 km

    Correct Answer: D

    Solution :

    (d): 600 km Let uniform speed be u and distance = d \[\frac{d}{u}=t\Rightarrow d=ut;\] Also, \[\frac{d}{u+10}=t-2;\frac{d}{u-10}=t+3\] \[\Rightarrow ut=(u+10)(t-2)\Rightarrow \cancel{ut}=\cancel{ut}+10t-2u-20\] \[\Rightarrow [\,u-5t=-10\,]\]?????????..(1) Also, \[\frac{ut}{u-10}=(t+3)\Rightarrow \cancel{ut}=\cancel{ut}-10t+3u-30\] \[\Rightarrow \,\,\,[\,3u-10t=30\,]\]????????.(2) From (1) and (2), \[5t=60\Rightarrow t=12\] And \[u=-10+60=50\] \[\therefore ut=50\times 12=600\]


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