# 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: 1/2 The most economical speed for this journey is :
 ✖ A. 20 km/hr ✖ B. 30 km/hr ✖ C. 35 km/hr ✔ D. 40 km/hr

Solution:
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.

## (2) Comment(s)

SIDDHARTH N
()

They are using (Time=Dist/Speed).

If you take the above formula for Total Cost as (Total cost = a*b), then

a is the total cost per hour and

b determines the total hours itself.