M and N can complete a certain project together in 36 days. After M works for 20 days, N is left to finish the remaining work by himself in 52 days. How many days would it take for N to complete the entire project on his own?

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1. Let N's time be $x$ days. Then N's rate is $1/x$ and M+N rate is $1/36$.
2. M's rate = $1/36 - 1/x = (x-36)/(36x)$. In 20 days M does $20*(x-36)/(36x)$.
3. Remaining work = $1 - 20*(x-36)/(36x) = (4x+180)/(9x)$. N finishes it in 52 days so $52*(1/x) = (4x+180)/(9x)$.
4. Solve $4x+180=52*9=468$, so $x=72$. Thus N alone takes 72 days.
FINAL_ANSWER: c

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