Question

If ${\log }_{10}x+{\log }_{10}y=2,x-y=15$, then which of the following is true?

• A. $(x,y)$ lies on the line $y=4x+3$
• B. $(x,y)$ lies on $y^2=4x$
• C. $(x,y)$ lies on $x=4y$
• D. $(x,y)$ lies on $4x=y$

Answer 1

The correct option is C $(x,y)$ lies on $x=4y$

${\log }_{10}x+{\log }_{10}y=2$, where $x,y>0$
$\Rightarrow {\log }_{10}xy=2[\because \log a+\log b=\log (ab\left)\right]$
$\Rightarrow xy={10}^2=100$
On solving $xy=200$ and $x-y=15$ , we get
$x=20,y=5$
Ans: C