Solution :
The effective resistance when connected in parallel is
$R^1= \large\frac{R_1R_2}{R_1+R_2}$
$\qquad= \large\frac{2 R_2 \times R_2}{2R_2 +R_2}=\frac{2}{3}$$R_2$
$\bigg[ \large\frac{R_1}{R_2} $$=2 \;or\; R_1 =2 R_2 \bigg]$
$\large\frac{2/3 R_2}{R_2} =\frac{t^1}{3}$$=2 minutes$
Answer : 2m