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JEE Main & Advanced JEE Main Online Paper (Held On 23 April 2013)

  • question_answer
                    The cost of running a bus from A to B, is \[\operatorname{Rs}.\left( \operatorname{av}\frac{\operatorname{b}}{\operatorname{v}} \right),\] where v km/h is the cost speed of the bus. When the bus travels at 30 km /h, the cost comes out to be Rs. 75 while at 40 km/h, it is Rs. 65 Then the most economical speed (in Km/h)of the bus is :     JEE Main Online Paper ( Held On 23  April 2013 )

    A)                   45                                        

    B)                                          50

    C)                                          60                                        

    D)                                          40

    Correct Answer: C

    Solution :

                      Let cost \[C=av+\frac{b}{v}\]                 According to given question, \[30a+\frac{b}{30}=75\]                                                                ?(i) \[40a+\frac{b}{30}=65\]                                                                ...(ii) On solving (i) and (ii), we get \[a=\frac{1}{2}\]and\[b=1800\] Now, \[C=av+\frac{b}{v}\]\[\Rightarrow \]\[\frac{dC}{dv}=a-\frac{b}{{{v}^{2}}}\] \[\frac{dC}{dv}=0\Rightarrow a-\frac{b}{{{v}^{2}}}=0\] \[\Rightarrow \]\[\frac{dC}{dv}=0\Rightarrow a-\frac{b}{{{v}^{2}}}=0\] \[\Rightarrow \]\[v=\sqrt{\frac{b}{a}}=\sqrt{3600}\]\[\Rightarrow \]\[v=60\,kmph\]


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