A began to do a job alone. After 6 days, he was joined by B. They both worked for another 5 days, after which they were joined by C. Three of them completed the work in a further period of 9 days. How long would C take to do the entire work alone, assuming that A and B separately could do the whole work in 36 days and 42 days, respectively?

Assuming the total work is the least common multiple of 36 and 42, which is 252 units, A's daily work is 7 units and B's is 6 units. A works for a total of 20 days (6 plus 5 plus 9), completing 140 units. B works for a total of 14 days (5 plus 9), completing 84 units. The work done by A and B is 224 units, leaving 28 units for C, who worked for 9 days. C's daily work is 28 divided by 9, so C alone would take 252 divided by (28/9) days. C takes 81 days to do the entire work alone.

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