An outlet pipe can empty a full cistern in 3 hours. In how much time will the same pipe empty exactly two-thirds of the cistern?

Introduction / Context:When rate is constant, time is directly proportional to the fraction of the job completed. Emptying two-thirds of a tank at a constant rate uses two-thirds of the full-emptying time.

Given Data / Assumptions:

• Full emptying time = 3 hours.
• Constant emptying rate; no refilling occurs during emptying.

Concept / Approach:Time for a fraction f of the work at constant rate equals f times the full time.

Step-by-Step Solution:Fraction to be emptied = 2/3.Full-emptying time = 3 hours.Required time = (2/3) * 3 = 2 hours.

Verification / Alternative check:Rate = 1 tank / 3 hours = 1/3 tank/hour. In 2 hours, volume emptied = (1/3) * 2 = 2/3 tank.

Why Other Options Are Wrong:3 h is for the entire tank; 4 h and 5 h exceed the full-emptying time, which is impossible here.

Common Pitfalls:Using inverse proportionality (incorrect in this direct fraction-time scenario).

Final Answer:2 h