Question

If the sum of two numbers is 24 and the sum of their reciprocals is $\frac{1}{6},$ then the difference of the numbers is .

• A. 0.0
• B. 12
• C. 6

Answer 1

The correct option is A 0.0

Let the numbers be $x$ and $y.$
$x+y=24\Rightarrow y=24-x$

The reciprocals of the numbers $x$ and $y$ are $\frac{1}{x}$ and $\frac{1}{y}=\frac{1}{24-x}$ respectively.

Then, by question

$\frac{1}{x}+\frac{1}{24-x}=\frac{1}{6}.$

$\Rightarrow \frac{24-x+x}{x(24-x)}=\frac{1}{6}$

$\Rightarrow 144=24x-x^2$

$\Rightarrow x^2-24x+144=0$

$\Rightarrow (x-12{)}^2=0$

Thus, 12 is a repeated root of the equation (repeated twice).
$\Rightarrow y=24-x=24-12=12$
$\Rightarrow x-y=12-12=0$
Thus, the difference of the numbers is zero.