# Moderate Algebra Solved QuestionAptitude Discussion

 Q. A Metro train from Mumbai to Gurgaon has capacity to board 900 people. The fare charged (in Rs) is defined by the function:  $f=\left(54-\dfrac{x}{32}\right)^2$  where $x$ is the number of the people per trip. How many people per trip will make the marginal revenue equal to zero?
 ✖ A. 1728 ✔ B. 576 ✖ C. 484 ✖ D. 364

Solution:
Option(B) is correct

The number of people per trip is $x$.

The fare for each person

$=\left(54-\dfrac{x}{32}\right)^2$

The revenue from $x$ people

$=x\left(54-\dfrac{x}{32}\right)^2$

Let

$g(x)=x\left(54-\dfrac{x}{32}\right)^2$

When the revenue is the maximum, the marginal revenue equal to zero.

$g'(x)=\left(54-\dfrac{x}{32}\right)^2-\dfrac{2x}{32}\left(54-\dfrac{x}{32}\right)$

For the maximum value of $g(x)$:

$g'(x)=0$

$\Rightarrow \left(54-\dfrac{x}{32}\right)=0$ and

$\left(54-\dfrac{3x}{32}\right)=0$

$\Rightarrow x=1728$, $x=576$

Given the capacity of the train is 900, the number of people per trip = 576

## (1) Comment(s)

Anurag
()

How to Calculate marginal revenue ?