A and B can do a piece of work in 10 days. B and C can do it in 12 days. A and C can do it in 15 days. How long will A take to do it alone?
[A]20 days
[B]24 days
[C]30 days
[D]40 days

24 days
(A + B)’s 1 day’s work $= \frac{1}{10}$
(B + C)’s 1 day’s work $= \frac{1}{12}$
(C + A)’s 1 day’s work $= \frac{1}{15}$
2(A + B + C)’s 1 day’s work $= \frac{1}{10}+\frac{1}{12}+\frac{1}{15} = \frac{6+5+4}{60} = \frac{1}{4}$
∴ (A + B + C)’s 1 day’s work $= \frac{1}{8}$
∴ A’s 1 day’s work $= \frac{1}{8}-\frac{1}{12} = \frac{3-2}{24} = \frac{1}{24}$