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

$12 \frac{1}{4}$

A+ = 10 hrs, B+ = 16 hrs,

⇒ They are opened alternatively started with A 

 1st hour = 8 units,

 2nd hour = 5 units,

Every 2 hours, 13 units of tank is filled,

So, in 12 hours, 78 units of tank is filled,

Therefore, in $12\frac{1}{4}$ hours, full 80 units of tank is filled.