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Approximately 1% of red blood cells are destroyed per day. I was wondering if we could derive this from the assumption that all red blood cells have a lifespan of 120 days.

I think we should assume that the concentration of red blood cells is constant and that red blood cells are continuously created and destroyed at a constant and equal rate.

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    Well, assuming a uniform distribution of age among red blood cells on any day, you would expect $\frac{1}{120}$ of the red blood cells to be destroyed. This is close enough to $1%$ to maybe think the $1%$ you have is an approximation to this figure. – Sarvesh Ravichandran Iyer Sep 24 '16 at 01:22

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The formula for the Mean Time to Faliure says that $t=\frac1p$, where $t$ is the lifetime of an object and $p$ is the fraction of objects that fail.

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