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Common Information

The cost of fuming the engine of an army tank is proportional to the square of the speed and Rs 64 per hour for a speed of 16km/hr. Other costs amount to Rs 400 per hour. The tank has to make a journey of 400km at a constant speed.

Q.

Common Information Question: 2/2

The total cost for the journey at this most economical speed is :

 A.

Rs 6,000

 B.

Rs 8,000

 C.

Rs 10,000

 D.

Rs 11,000

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Solution:
Option(B) is correct

\(\begin{align*} Cost&=k^2\times speed^2[\text{ Where k is constant}]\\ 64&=k\times 16\times16\\ k&=\dfrac{1}{4}\\ cost&=\dfrac{speed^2}{4}\\ \end{align*}\)

\(\text{total cost}=\left[\dfrac{speed^2}{4}+400\right]\times 400/speed\)

using options, putting different values of speed, we find speed = 40km/hr to be most economical.


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