# 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 :

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 :
[A]$15\frac{2}{3}$ days
[B]5 days
[C]10 days
[D]$7\frac{5}{6}$ days

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