A and B together can do a piece of work in 3 days. If A does thrice as much work as B in a given time, find how long A alone would take to do the work ?

If A does thrice as much work as B, then A's work rate is 3 times B's. Let B's rate = 1 unit/day, so A's rate = 3 units/day. Combined rate = 4 units/day. If they complete work in 3 days, total work = 4 × 3 = 12 units. A alone would take 12/3 = 4 days. This is a work-rate problem where efficiency ratios determine individual times.