Manoj takes twice as much time as Ajay and thrice as much as Vijay
Manoj takes x days ,Ajay takes x / 2 days and vijay takes x / 3 days
together they work then finished in 1 day
1 / x + 2 / x + 3 / x = 1
6 / x = 1
x = 6
So, manoj takes 6 days to complete work.