A large water tank gets filled from two pipes $$T_1$$ and $$T_2$$. $$T_1$$ alone can fill it in 50 minutes, while $$T_2$$ alone can fill it in one hour. If on any day $$T_2$$ starts working only after $$T_1$$ has been used for filling half the tank, then the time taken to fill the tank will be

A

$$50 + \frac{61}{2}$$ minutes

B

$$110$$ minutes

C

$$\frac{1}{2}\left[\frac{1}{50} + \frac{1}{60}\right]$$ minutes

D

$$\frac{150}{11} + 25$$ minutes