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 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.