11th Class Mathematics Other Series Question Bank Critical Thinking

  • question_answer A boy goes to school from his home at a speed of x km/hour and comes back at a speed of y km/hour, then the average speed is given by  [DCE 2002]

    A) A.M.

    B) G.M.

    C) H.M.

    D) None of these

    Correct Answer: C

    Solution :

     Let, the distance of school from home = d and time taken are \[{{t}_{1}}\]and t2. \[\therefore {{t}_{1}}=\frac{d}{x}\] and \[{{t}_{2}}=\frac{d}{y}\] Avg. velocity =\[\frac{\text{Total}\,\text{dis}\text{tance}}{\text{Total}\,\text{time}}\] \[=\frac{2d}{\left( \frac{d}{x}+\frac{d}{y} \right)}=\frac{2xy}{x+y}\], which is the H.M. of x and y.

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