Raju, Sunil and Vishal can separately finish a work in 20, 30 and 40 days, respectively. In how many days Raju can finish the work, if he is assisted by Sunil and Vishal on alternate days, starting with Sunil?

$12\frac{3}{5}$

Efficiency ∝ $\frac{1}{time}$

                   Raju  :  Sunil  :  Vishnu 

Time              20   :     30  :     40

Efficiency         6   :     4    :     3

Let the total work be 120 

Since Raju is Sunil and Vishnu on alternate days, 

The efficiencies will be as follows:

10, 9, 10, 9, 10..................

In 12 days, 114 units of work will be complete 

The remaining work i.e. 6 units will be completed by Raju and Sunil together in $\frac{6}{10}$ = $\frac{3}{5}$ days

Total time taken = 12$\frac{3}{5}$  days