Question

The difference between two positive numbers $x$ and $y$ $(x>y)$ is $4$ and the difference between their reciprocals is $\frac{4}{21}$. Then the numbers are

• A. $7,3$
• B. $8,4$
• C. $9,5$
• D. $10,6$

Answer 1

The correct option is A $7,3$

According to the problem,

$(x-y)=4$....................(1)

and

$(\frac{1}{y}-\frac{1}{x}=\frac{4}{21})$

$\Rightarrow \left(\frac{x-y}{xy}\right)=\frac{4}{21}$

$\Rightarrow xy=\frac{21}{4}\cdot (x-y)$

$\Rightarrow xy=\frac{21}{4}\cdot 4$..................using (1)

$\Rightarrow xy=21$

$\Rightarrow x(x-4)=21$...............From(1)

$\Rightarrow x^2-4x-21=0$

$\Rightarrow (x+3)(x-7)=0$

Since $x>0$ then $x=7$.

Then $y=3$

The numbers are $7,3$.