Question

Vijay inherited huge wealth from his father and by establishing a soft drinks company, he squared his wealth. He started a company which manufactures airplane toys and incurred huge losses amounting to $k(>0)$ times the wealth he inherited from his father. His total assets now stand at debt of Rs. 4 crore. For what value of $k$ is this scenario possible?

• A. Any value of $k$ is possible
• B. Depends on what amount is inherited initially, i.e. $x$
• C. $k$ is any value greater than or equal to 4
• D. None of these

Answer 1

The correct option is C

$k$ is any value greater than or equal to 4

Let the wealth inherited by Vijay be Rs. $x$ crores.
His wealth becomes $x^2$ because of the soft drinks company.
But the toys manufacturing company brought a loss of $kx$.
Now, the wealth of Vijay is $x^2-kx$.
This is mentioned to be equal to $-4$ crores [minus sign, because it is a debt]
$\Rightarrow x^2-kx=-4$
$\Rightarrow x^2-kx+4=0$
For this scenario to be possible, $D\ge 0\Rightarrow k^2-16\ge 0$
$\Rightarrow k^2\ge 16$
$\Rightarrow k\ge 4$ or $k\le -4$

$\because k>0\therefore k\ge 4$
So the correct option is $k$ is any value greater than or equal to 4.