$A,B$ and $C$ can do a job in $12,5$ and $20$ days respectively. How long will they take to complete the work together?

Given that,

$A=12$days

$B=5$ days

$C=20$ days

Let the total work be $60$ days (By taking L.C.M of 12,5,20)

$A$ can do $5$ work per day

$B$ can do $12$ work per day

$C$ can do $3$ work per day

We know that,

Total work formula $=\frac{a.b.c}{ab+bc+ca}$

$\begin{array}{c}=\frac{12\times 5\times 20}{12\times 5+5\times 20+20\times 12}\\ =\frac{12\times 5\times 20}{60+100+240}\\ =\frac{1200}{400}\end{array}$

Therefore,

Total work take to complete together is $3$ days.