A can do a piece of work in 20 days B in 30 days and C in 60 days All of them begin to work together...........

Quantitative Aptitude (CGL) Time and work

A can do a piece of work in 20 days, B in 30 days and C in 60 days. All of them begin to work together. However A left the job after 6 days and B quit work 6 days before the completion of the work. How many days did the work last?

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Explanation:

A can do a piece of work in 20 days; or, he does 1/20th of the work in a day. Similarly, B does 1/30th of the work per day, and C does 1/60th. After 6 days, they have done 6/20+6/30+6/60, or 3/5ths of the work, leaving 2/5ths to be done. Now, let n be the amount of days C kept working, and n-6 be the amount of time B kept working. Then:
n/60 + n-6/30=2/5
n+2(n-6)=24
3n=36
n=12