Aptitude Discussion

**Common Information**

The cost of fuel for running the engine of an army tank is proportional to the square of the speed and Rs. 64/hour for a speed of 16 kmph. Other costs amount to Rs. 400/hour. The tank has to make a journey of 400 km 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

Cost of fuel is proportional to square of the speed:

\(E=KS^2\)

\(\Rightarrow E=64 \text{ and } S=16 \)

\(K=\dfrac{1}{4}\)

Total cost

\(=\dfrac{1}{4}\times S^2t+400t\)

Most economical speed, checking options we get most economical speed at 40km/hr.

Total cost at 40km/hr

\(=\dfrac{1}{4}\times 40^2+400\left(\dfrac{400}{40}\right)\)

\(=\text{Rs }8,000\)

**Bhumit**

*()
*

It should be 4000 + 400 = 4400 !!