Two pipes A and B can fill an empty tank in 10 hours and 16 hours respectively. They are opened alternatively for 1 hour each. If pipe B open first, then in how many hours, will the empty tank be filled?

12\(\frac{2}{5}\)

Total efficiency of A+B = 13 units  in 2 hour 

Total work = efficiency × time

Total work done by A & B together in  (6 × 2 )  hours = 13 × 6 = 78 units 

After 12 hours , 2 units are yet to be filled . 

On, 13th hour B will be opened , time taken = \(\frac{work}{efficiency}\) =  \(\frac{2}{5}\)

So, tank will be filled in =  12\(\frac{2}{5}\)