Question

Vijay inherited his father's wealth and doubled it by starting a soft drinks company. He then started a company which manufactures airplane toys and incurred losses amounting to $k(>0)$ times the wealth he inherited. If his total assets now stand at a debt of 4 crores, then ___.

• A. $k^2<16$
• B. $k^2<4$
• C. $k<4$
• D. $k\ge 4$

Answer 1

The correct option is D $k\ge 4$

Let the wealth inherited by Vijay be $x$ crores. His wealth became $x^2$ crores due to the soft drinks company. But the toys manufacturing company brought a loss of $kx$ crores. Thus, money left with him equals $x^2-kx,$ which is equal to 4 crores, by question.
i.e., $x^2-kx=-4$
$\Rightarrow x^2-kx+4=0$
For this scenario to be possible, the quadratic equation must have real roots.
$⟹D\ge 0$
$\Rightarrow k^2-16\ge 0$
$\Rightarrow k^2\ge 16$
$\Rightarrow k\ge 4(\because k>0)$
Thus, the value of $k$ is greater than or equal to 4.