Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. If only pipe B was kept open in the beginning for $$\frac{1}{5}$$th of the total time and then. both pipe A and B were kept open for the remaining time. How many minutes did it take the pipes to fill the tank?

A

$$13\frac{5}{23}$$

B

$$16\frac{5}{23}$$

C

$$16\frac{1}{23}$$

D

$$13\frac{1}{23}$$