Some staff promised to do a job in 15 days but 6 of them went on leave. So the remaining men took 20 days to complete the job. How many men were there originally?

24

Let there were originally x men.

Total work = efficiency × number of days

Total work  = 15 × x = 15x

6 went on leave . So leftover men does the work in 20 days 

total work by them = 20(x - 6)

As per questions,

15x = 20(x - 6)

15x = 20x - 120

 15x - 20x = -120

-5x = -120

 x = 24  is number of men