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  • The cost of running a bus from A to B is Rs. <img alt="\left ( av+\frac{b}{v} \right )" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%20%28%20av&plus;%5Cfrac%7Bb%7D%7Bv%7D%20

The cost of running a bus from A to B is Rs. \left ( av+\frac{b}{v} \right ), where v km/h is average 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:

Option: 1

45


Option: 2

50


Option: 3

60


Option: 4

40


Answers (1)

best_answer

Let cost C = \left ( av+\frac{b}{v} \right )

According to the question

\begin{aligned} &30 a+\frac{b}{30}=75\;\;\;\;\;\;\;\;\;\;\;\;\;\ldots(i)\\ &40 a+\frac{b}{40}=65\;\;\;\;\;\;\;\;\;\;\;\;\;\ldots(ii) \end{aligned}

a = 1/2 and b = 1800

\\\text { Now, } C=a v+\frac{b}{v} \\ \Rightarrow \frac{d C}{d v}=a-\frac{b}{v^{2}} \\ \frac{d C}{d v}=0 \Rightarrow a-\frac{b}{v^{2}}=0 \\ \Rightarrow v=\sqrt{\frac{b}{a}}=\sqrt{3600} \\ \Rightarrow y=60 \mathrm{ \;kmph}

Posted by

Ritika Harsh

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