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Question

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


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