This didn't actually happen

Algebra Level 5

My father had to wash some nappies in a strong bleach solution and wanted to rinse them out so that they contained as small a concentration of bleach as possible. He can wring the nappies out so there is just half a litre of liquid left. He wrings the nappies out after washing them in the bleach, adds 12 litres of water, mixes thoroughly, wrings them out again, adds a further 8 litres of water, and mixes thoroughly, reducing the concentration of bleach to $$\dfrac {1}{k}$$ of its original. Find $$k$$.

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