Question

Two numbers are such that their difference is 5 and their product is 100 times their difference, the numbers are____.

• A. (12,7)
• B. (11,6)
• C. (13,18)
• D. (20,25)

Answer 1

The correct option is D (20,25)

$Letthenumbersbex.y$
$Accordingtoquestion$
$x-y=5.............\left(i\right)$
$100(x-y)=xy..........\left(ii\right)$
$100(5+y-y)=(5+y)yfrom\left(i\right)$
$\Rightarrow 500=5y+y^2$
$\Rightarrow y^2+5y-500=0$
$\Rightarrow (y+25)(y-20)=0$
$y=20,-25$
$pluggingin\left(i\right)$
$x-20=5$
$x=25$
$Hencenumbersare20,25$