well here is how i go about it,
first of all i basically try to figure out how much percent of the total work can be done by A/B/C (etc) per time unit specified (hrs/days/weeks etc.)
so if we get this info, A can complete painting a wall in 12 days, then % of wall he can paint in one day would be 8.5%
and also if B can complete painting a wall in 20 days, then % of wall B can paint in one day would be 5%.
Now with this info we can do any combination in seconds
like A paints for 2 days, then B joins in. How much more time will it take them now?
in 2 days A paints 8.5 x 2 = 17%.
A and B together paint 8.5 + 5 % of the wall per day = 13.5% of the wall per day
So % of wall left is 83%, per day can be painted 13.5% . no of days we need = 83/13.5 which will be close to one of the options you have. (very bad numbers to take for an example
you can apply this to any kind of work related probs. I prefer dealing with %ages rather than fractions.
Just ask urself what can be done faster :- (1/15 + 3/5 + 1/20) or (6.66% + 60% + 5%)?
Thats just my approach, i know there are better ones .
The Legion dies, it does not surrender.