# Moderate Ratios & Proportion Solved QuestionAptitude Discussion

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

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.