Applications Of Derivatives Question 414
Question: The cost of running a bus from A to B, is Rs. $ ( av+\frac{b}{v} ), $ where v km/h is the 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:
Options:
A) 45
B) 50
C) 60
D) 40
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Let cost $ C=av+\frac{b}{v} $ According to given question, $ 30a+\frac{b}{30}=75 $ -(i) $ 40a+\frac{b}{40}=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 v=\sqrt{\frac{b}{a}}=\sqrt{3600} $
$ \Rightarrow v=60kmph $
BETA
