Question

The cost of running a bus from A to B, is $\operatorname{Rs}\left(a v+\frac{b}{v}\right)$, where $v k \cdot m / hr$. is the average speed of the bus. when the bus travels at $30 k . m / hr$., the cost comes out to be Rs. 75 while at $40 k . m / hr$., it is Rs. 65 . The most economical speed (in k.m/hr.) of the bus is

• A. 30
• B. 40
• C. 45
• D. 60

Answer 1

Answer: (D)

Here $a =\frac{1}{2}, b =1800$. Now, $c ( v )=\frac{ v }{2}+\frac{1800}{ v } \Rightarrow c ^{\prime}( v )=0 \Rightarrow v =60 k \cdot m / hr$.
Also, $\left.\frac{ d ^2 c }{ dv ^2}\right]_{ v =60}=$ positive quantity.
$\therefore c_{\text {min. }}(v=60)=60$