In a factory, Ajay and Vijay work on the same machine to cut diamonds but on alternate hour basis. Ajay works for the first hour and then Vijay works for the second hour and so on. Ajay can complete the work in 6 hours, while Vijay completes it in 16 hours if they work individually. In how much time can they complete the work if they are using the machine on alternate basis?

8 h 30 min

AJAY = 6hrs, VIJAY = 16hrs,

Working on alternate hours, starting with AJAY,

1st hour       = 8 units

2nd hour      = 3 units

Every 2 hrs   = 11 units

Hence, in 8 hrs, 44 units of work will be completed.

The remaining work i.e; 4 unit will be completed by VIJAY in = \(\frac{4}{8}\) = \(\frac{1}{2}\) hrs.

Therefore,

 The Total hours taken to complete work = 8 + \(\frac{1}{2}\) = \( {8 }_{ 2}^{ 1} \) hrs. = 8 h 30 minutes.