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 most economical speed for this January is: |

✖ A. |
10 kmph |

✖ B. |
20 kmph |

✖ C. |
35 kmph |

✔ D. |
40 kmph |

**Solution:**

Option(**D**) 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.

**Edit:** A typo has been corrected in the question after it has been pointed out by **Sai Rajesh.**

**Sai Rajesh**

*()
*

Thank you Sai Rajesh for pointing it out, corrected the typo.

Please correct "Rs. 64 hour" to Rs. 64 per hour or Rs. 64 / hour & similarly "Rs. 400 hour" to Rs. 400 per hour or Rs. 400 / hour.