Ratios & Proportion
Aptitude

 Back to Questions

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

 Hide Ans

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.



Bharadwaj
 ()

Hi, why is it being multiplied by 400. This is the cost/hour correct? So it has to be multiplied by the number of hours. Im not sure if Im wrong here. Can you please explain that.