A and B can do a work in 12 days, B and C in 15 days and C and A in 20 days. If A, B and C work together, they will complete the work in :

10 days
According to question,
A and B can do a work in 12 days
∴ (A + B)’s one day’s work $latex = \frac{1}{12}&s=1$
Similarly, (B + C)’s one day’s work $latex = \frac{1}{15}&s=1$
and (C + A)’s one day’s work $latex = \frac{1}{20}&s=1$
On adding all three,
∴ 2 (A + B + C)’s one day’s work $latex = \frac{1}{12}+ \frac{1}{15}+ \frac{1}{20}&s=1$
$latex = \frac{10+8+6}{120} = \frac{1}{5}&s=1$
and (A + B + C)’s one day’s work $latex = \frac{1}{10}&s=1$
∴ A, B and C together can complete the work in 10 days.