Efficiency of $A:3,$ efficiency of $B:1$
Then Time of $A:1,$ time of $B: 3$
Given that $3-1 = 2 \implies 60$ days
Time of $A:30$ days, time of $B: 90$ days
Total work $ = LCM(30,90) = 90$ unit/day
If $A\&B$ working together then,$\text{Time} = \dfrac{\text{Total work}}{\text{Efficiency of A and B}} = \dfrac{90}{4} = 22.5$ days.
$$\text{(OR)}$$
If persons $M_{1}$ can do $W_{1}$ work in $D_{1}$ days working $T_{1}$ hours in a day and $M_{2}$ Persons can do $W_{2}$ work in $D_{2}$ days working $T_{2}$ hours in a day then the relationship between them is
$$\dfrac{M_{1}D_{1}T_{1}}{W_{1}} = \dfrac{M_{2}D_{2}T_{2}}{W_{2}}$$
Given that, $A = 3B\;\text{(Efficiency)},B = 3A\;\text{(Time)}$
Now, $\dfrac{A\; (x-60) \;\text{days}}{W} = \dfrac{B\;x\;\text{days}}{W}$
$\implies 3B(x-60) = B x $
$\implies x = 90$ days.
$\therefore B = 90$ days, $A = 30$ days.
One day work of $A = \dfrac{1}{30}$ unit/day, One day work of $B = \dfrac{1}{90}$ unit/day (Efficiency)
When they work together, then $A+B = \dfrac{1}{30} + \dfrac{1}{90} = \dfrac{4}{90}$ unit\day
$\therefore$ Time taken by $A\&B$ together is $ = \dfrac{90}{4} = 22.5$ days.
So, the correct answer is $(B).$