A and B together can do a piece of work in 20 days. B and C together can do the same of work in 25 days. C and A together can do the same work in 15 days. In how many days A alone can do the same work?

$\frac{600}{23}$

A + B = 20 days,

B + C = 25 days,

A + C = 15 days,

⇒ Adding all the efficiencies,

⇒ 2(A + B + C) = 47

⇒ A+ B+ C = \(\frac{47}{2}\) = 23.5 

⇒ A + 12 = 23.5

⇒ A = 23.5 - 12 = 11.5 

Therefore, A alone will complete the total work in =  \(\frac{300}{11.5}\) = \(\frac{600}{23}\) days.