When people (or machines, etc) work together, theirratesadd.

"A,B and C can complete a work in 12,15 an 20 days respectively."

So A's rate of work is "one job in 12 days" or 1/12 job per day. Similarly, B's rate is 1/15 job per day and C's is 1/20 job per day. Together they can do 1/12+ 1/15+ 1/20 job per day. 12= 4(3), 15= 5(3) and 20= 4(5) so the least common denominator is 3(4)(5)= 60. 1/12+ 1/15+ 1/20= 5/60+ 4/60+ 3/60= 12/60= 1/5 job per day. So you were right- at 1/5 job per day, they will complete the job in 5 days.

"If they start the work together,and C leaves for 2 days,then how long will it take for A and B to do the work together?"

So all three, A, B, and C, work for three days, at 1/5 job per day and so compete 3/5 of the job, leaving 2/5 of the job still to be done.

A and B working together, without C, have rate 1/12+ 1/15= 5/60+ 4/60= 9/60= 3/20 job per day.

At 3/20 job per day, how long will it take them to do 2/5 job?