We know that number of days taken to work is reciprocal of the rate of the work.

Rates of working of two taps A and B are in the ratio 2:3

∴ Work done by A: \(\frac{1}{2}\)

Work done by B: \(\frac{1}{3}\)

∴ Ratio of work done is \(\frac{1}{2}:\frac{1}{3}=3:2\)