A, B and C can finish a task in 42 days, 84 days and 28 days, respectively. A started the work. B joined him after 3 days. If C joined them after 5 days from the beginning, then for how many days did A work till the completion of the task?

$$\frac{\left(Remaining\ work\right)}{Total\ effeciency}=\ \frac{72}{\left(2+1+3\right)}=\frac{72}{6}=\ 12$$Let the total work be LCM(42,84,28) = 84

Efficiency of A = $$\frac{84}{42}=2$$

Efficiency of B = $$\frac{84}{84}=1$$

Efficiency of C = $$\frac{84}{28}=3$$

A worked initially for 3 days = $$2\times\ 3=6$$

Now, A and B worked together for 2 days = $$\left(2+1\right)\times\ 2=6$$                           

Remaining work = 84 - (6 + 6) = 72

Now the remaining work will be done by A, B and C together 

i.e $$\frac{\left(Remaining\ work\right)}{Total\ effeciency}=\ \frac{72}{\left(2+1+3\right)}$$

i.e $$\frac{72}{6}=\ 12$$

Initially A worked for 3 days alone and 2 days with B , 

So finally A took time till the completion of the task is= 5+12=17 days