Question

The sum of two numbers is 1000 and the difference between their squares is 256000, then the numbers are: (a) 616 and 384 (b) 628 and 372 (c) 564 and 436 (d) none of these. ​

Answer 1

To find : missing numbers

Given : The sum of two numbers is $1000$ and difference between their squares is $256000$ .

Solution :

• Let missing numbers be $x$ and $y$ .
• According to given data we write given condition as ,

       $\begin{array}{l}\Rightarrow x+y=1000 ---------- (i) \\\Rightarrow x^{2}-y^{2}=256000\end{array}$

• Applying identity $x^{2} - y^{2} = ( x + y ) ( x -y )$

       $\begin{array}{l}\Rightarrow 1000 \times (\mathrm{x}-\mathrm{y})=256000 \\\Rightarrow \mathrm{x}-\mathrm{y}=256 \end{array}$  -------------------------(ii)

• Adding equation (i) and (ii) we get ,

        $\Rightarrow 2 \mathrm{x}=1256 \Rightarrow \mathrm{x}=628$

• Put the value of $x$ in (i)  

      $\Rightarrow 628+\mathrm{y}=1000 \Rightarrow \mathrm{y}=372$

Hence , two numbers are , $628$ and $372$ .