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Answer: 10 more games


The number of games lost
$49\%\times500 = 250-5 = 245$ games won
$\therefore 255$ games lost

Win more games $\therefore$ number of games lost is still $255$

$50\%$ win means $50\%$ loss so $255=50\%$ of total number of games

$255\times2 = 510$ which is $10$ more than $500$


Using balance
                               $500\times49\%\qquad+\qquad? \times100\%$ has an average of $50\%$
                                       $\nearrow$                          $\nearrow$
                               $1\%$ from $50\%$        $50\%$ from $50\%$
                                       $\uparrow$                            $\uparrow$                         
    Need $50$ times more of these              than of these

So $50$ times fewer than $500$
$500\div50=10$
$10$ more games

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.