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
Time taken by $$T_1 and T_2$$ together to fill the tank = $$\frac{1}{\frac{1}{50} + \frac{1}{60}} \frac{300}{11}$$ minutes
Time taken by $$T_1 and T_2$$ together to fill half the tank = $$\frac{300}{2 * 11} = \frac{150}{11}$$ minutes
Time takne by $$T_1$$ alone to fill half the tank = $$\frac{50}{2} = 25$$ minutes
Total time taken to fill the tank completely = 25 + $$\frac{150}{11}$$ minutes