A, B and C can complete a piece of work separately in 10, 20 and 40 days, respectively. In how many days will the work be completed if A is assisted by both B and C every third day?

$8\frac{2}{7}$

A = 10D, B = 20D, C = 40D,

Since A is working daily and B & C assist him on every third day, the efficiencies will be as follows:

1st day (A) = 4 units

2nd day (A) = 4 units

3rd day (All) = 4 + 2 + 1 = 7 

Every 3 days work = 4 + 4 + 7 = 15

Hence, in 6 days, 30 units of work will be completed

and in 8 days. 38 units of work will be completed.

The remaining work i.e; 2 units will be completed by all of them in = \(\frac{2}{7}\) days.

Therefore, The Total time taken to complete work will be = 8 + \(\frac{2}{7}\) 

= \( { 8}_{ 7}^{ 2} \)days.