In a partnership firm two partners, Vijay and Praveen are working on an assignment. It will take 12 weeks for Vijay to complete the entire assignment alone, while Praveen will take 8 weeks to complete it alone. Due to work pressure, they decided to work on that assignment on the alternate week basis. In the first week Praveen will work and in the second week Vijay will work and so on. In how many weeks the work will be completed if they work on alternate week basis?

9.5

VIJAY = 12 WEEKS, PRAVEEN = 8 WEEKS 

Working on alternate weeks, starting with Praveen

1st week (Praveen) = 3

2nd week (Vijay) =    2

Every 2 weeks work = 5 

Hence, in 9 weeks, 23 units of work will be completed.

The remaining work i.e; 1 unit will be completed by Vijay in = \(\frac{1}{2}\) weeks.

Therefore, The Total weeks taken to complete work will be 9 + \(\frac{1}{2}\) = \( {9}_{2 }^{ 1} \) = 9.5 weeks.