10th Class Mathematics Solved Paper - Mathematics-2018

  • question_answer A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100 km/h from the usual speed. Find its usual speed.


    Let the usual speed of plane be x km/h. Increased speed = (x+100) km/h.
    \[\therefore \] Distance to cover \[=1500\text{ }km\]
    Time taken by plane with usual speed \[=\frac{1500}{x}hr.\]
    Time taken by plane with increased speed
    According to the question,
                            \[1500\left[ \frac{1}{x}-\frac{1}{x+100} \right]=\frac{1}{2}\]
                            \[1500\left[ \frac{x+100-x}{(x)(x+100)} \right]=\frac{1}{2}\]
                                         \[\frac{1500\times 100}{{{x}^{2}}+100x}=\frac{1}{2}\]
                Either                       \[x+600=0\]
                                                         \[x=-600\] (Rejected)
                Or                            \[x-500=0\]
                \[\therefore \] Usual speed of plane = 500 km/hr.


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