Given total number of rats = 999919
999919 = 1000000 - 81 =
$\left({1000}^{2}-{9}^{2}\right)$ = (1000+9)(1000-9) = 1009 x 991.
Since there were more rats than there were cats, 991 cats killed 1009 rats each.
Let $\frac{1}{3}\left(10\right)=x$
=> 3x = 10
Given that $\frac{1}{2}\left(5\right)=3$
Therefore, $\frac{5}{2}x=10$
=> x = 10/3 = 4.
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