A tap can fill a cistern in 8 hours and another tap can empty it in 16 hours. If both taps are opened simultaneously from empty, what is the time (in hours) required to fill the cistern?

Introduction / Context:Opening a filler and an emptier together produces a net rate equal to their difference. If the filler is faster, the cistern will fill, albeit more slowly than with the filler alone.

Given Data / Assumptions:

• Filler: 8 hours ⇒ +1/8 tank/hour.
• Emptier: 16 hours ⇒ −1/16 tank/hour.

Concept / Approach:Net rate = 1/8 − 1/16 = 1/16 tank/hour. Time = 1 ÷ (1/16) = 16 hours.

Step-by-Step Solution:Compute: 1/8 − 1/16 = 2/16 − 1/16 = 1/16.Time = 16 hours.

Verification / Alternative check:In 16 hours, filler adds 2 tanks; emptier removes 1 tank; net = 1 tank filled.

Why Other Options Are Wrong:8 or 10 hours would imply a faster net rate than 1/16; 24 hours would be slower than the computed net rate.

Common Pitfalls:Adding times or forgetting the outlet’s negative contribution.

Final Answer:16