Question

The sum of two numbers is $1000$ and the difference between their squares is $256000$. Find the numbers

• A. $600,400$
• B. $628,372$
• C. $675,325$
• D. $728,262$

Answer 1

The correct option is B $628,372$

Let the numbers are $x$ and $y$
According to the question
$\Rightarrow x+y=\mathrm{1000.....}eq1$
$\Rightarrow x^2-y^2=256000$
$\because x^2-y^2=(x+y)(x-y)$
$\Rightarrow 1000\ast (x-y)=256000$
$\Rightarrow x-y=\mathrm{256.....}eq2$
Adding $eq1$ and $eq2$
$\Rightarrow 2x=1256\Rightarrow x=628$
Put the value of $x$ in $eq1$
$\Rightarrow 628+y=1000\Rightarrow y=372$
The numbers are $628$ and $372$