Aptitude 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. |
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.

**SIDDHARTH N**

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**Bharadwaj**

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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.

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.