P and Q together can complete a job in 16 days. Q and R together can complete it in 24 days, and R and P together can do it in 32 days. In how many days can P alone complete the job?

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1. Let the work rates be $p,q,r$ (jobs per day). Given: $p+q=\frac{1}{16}$, $q+r=\frac{1}{24}$, $r+p=\frac{1}{32}$.  
2. Add all three: $2(p+q+r)=\frac{1}{16}+\frac{1}{24}+\frac{1}{32}=\frac{13}{96}$. So $p+q+r=\frac{13}{192}$.  
3. Then $p=(p+q+r)-(q+r)=\frac{13}{192}-\frac{1}{24}=\frac{5}{192}$.  
4. Time for P alone $=\frac{1}{p}=\frac{192}{5}=38.4$ days. So choose **(c)**.  
FINAL_ANSWER: c

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