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

Solution

The correct option is B $$628,\,372$$Let the numbers are $$x$$ and $$y$$According to the question$$\Rightarrow x+y=1000.....eq1$$$$\Rightarrow x^{2}-y^{2} =256000$$ $$\because x^2-y^2=\left ( x+y \right )\left (x-y \right )$$$$\Rightarrow 1000\ast \left (x-y \right )=256000$$$$\Rightarrow x-y=256.....eq2$$Adding $$eq1$$ and $$eq2$$$$\Rightarrow 2x=1256\Rightarrow x=628$$Put the value of $$x$$ in $$eq 1$$$$\Rightarrow 628+y=1000\Rightarrow y=372$$The numbers are $$628$$ and $$372$$Mathematics

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