we know that,
Number of days A required to do piece of work = 10 days
Number of days B required to do piece of work = 12 days
Number of days C required to do piece of work = 15 days
∴ We can calculate, work done by A in 1 day = 1/10
Work done by B in 1 day = 1/12
Work done by C in 1 day = 1/15
Now, work done by A,B and C together in 1 day= 1/10 + 1/12 +1/15 = 15/60 = 1/4
∴ They can do work together in 4 days