Pipe A fills an empty cistern in 69 hours and pipe B drains a full cistern in 46 hours. Starting from a full cistern, the pipes are opened one hour each in turn, beginning with B. How long until the cistern is empty?

1. In one 2-hour cycle (B then A), net change = −1/46 + 1/69 = −1/138 of the tank. 2. After 135 cycles (270 hours), level remaining = 135 × (3/138) − 134 × (2/138)... taken as level = 3/138 just before the next B-hour. 3. The next B-hour drains exactly 3/138, emptying the tank: total = 270 + 1 = 271 hours = 11 days 7 hours. _Source: RRB Group D CEN-02/2018 PYQ, Q.35._