Question 688817
Let x=number of additional days it will take after the 24 more painters join in.

If 6 painters can complete the job in 45 days, then the job takes 6*45=270 painter-days to complete.  In other one painter can complete the job in 270 days 
In 10 days, 6 painters have completed 60 painter-days of work leaving 210 painter-days to be completed
OK now after 10 days, we have 24+6=30 painters to do 210 painter-days of work 
So, our equation to solve is:
30x=210
x=7 days---------------additional days it will take after 24 more painters join in
CK
In 7 day, 6 painters do 6*7=42 painter-days of work
In 7 days,24 painters do 7*24=168 painter-days of work
42+168=210
210=210

Hope this helps----ptaylor