Ratios & Proportion

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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.


Common Information Question: 1/2

The most economical speed for this journey is :


20 km/hr


30 km/hr


35 km/hr


40 km/hr

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Option(D) 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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