Aptitude Discussion

Q. |
Fortuner, the latest SUV by Toyota Motors, consumes diesel at the rate of $\dfrac{1}{400} \times \left[ \dfrac{1000}{x} + x \right]$ litres per km, when driven at the speed of $x$ km per hour. If the cost of diesel is Rs 35 per litre and the driver is paid at the rate of Rs 125 per hour then find the approximate optimal speed (in km per hour) of Fortuner that will minimize the total cost of the round trip of 800 kms? |

✔ A. |
49 km per hour |

✖ B. |
55 km per hour |

✖ C. |
50 km per hour |

✖ D. |
53 km per hour |

**Solution:**

Option(**A**) is correct

Given that the diesel consumption is at the rate

$\dfrac{1}{400}\times \left[\dfrac{1000}{x} + x \right]$

Cost of diesel = Rs 35 per litre

Payment to the driver = Rs 125 per hour.

Also given that the SUV is driven at the speed of $x$ km per hour.

Total cost $(c)$

\(=\dfrac{1}{400}\times \left[\dfrac{1000}{x} + x\right]\times 800\times 35+125\times \dfrac{800}{x}\)

\(=\dfrac{70000}{x}+70x+\dfrac{100000}{x}\)

Now differentiating both sides in the above equation with respect to $x$.

\(\dfrac{dc}{dx}=-\dfrac{170,000}{x^2}+70=0\)

⇒ $x= \textbf{49 km per hour.}$

**Akash Sarda**

*()
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Calculate the expression.

The expression is proportional to x^2. Therefore minimum of all the options is the answer.