First data: 45 men complete a work in 16 days.
Second data: 6 days after they started working 30 more men joined them.
Final question: how many days they will need to complete to finish remaining work?
mens * days = total work
One man do work in one day=1/720
45 men’s one day work(within 6 days) 1/16
Within 6 days they complete job=days*one day work=6*1/16=6/16=3/8
See the time and work formula
75 men do work in single day=total no of man/(total work)=75/720=5/48
Days * per day work = total work
They will need 6 days to complete reaming work Reference form R.S Aggarwal Book