What does the concept of 'man-days' represent, and how is it used to solve work problems?
Man-days represent total work effort (Number of workers × Days). It remains constant if work is constant, allowing calculation of required days with different worker counts.
In pipes and cisterns problems, how is the net rate of filling or emptying a tank calculated when both inlets and outlets are open?
Net rate = (Sum of filling rates) - (Sum of emptying rates). The tank fills if net rate is positive and empties if negative.
What is the core analogy between 'Pipes & Cisterns' and 'Time & Work' problems?
Filling a tank is analogous to positive work. Emptying a tank (or a leak) is analogous to negative work. Rates are additive/subtractive similarly.
Describe the strategy for solving 'Alternating Work' problems where people work in turns on different days.
Calculate work done in one complete cycle (e.g., A's day + B's day). Find how many full cycles fit in total work, then handle the remaining partial work.
How do you approach 'Leaving/Joining Midway' problems where team composition changes during the work?
Break the timeline into distinct phases where the working group is constant. Calculate work done in each phase sequentially until total work is completed.
What is the purpose of the LCM method in time and work problems, and how is it applied?
The LCM method avoids fractions by assuming the total work is the LCM of the individual time taken. Individual rates then become simple integers (LCM/Time).
In a scenario with a drain (negative work), how do you determine if a tank will eventually fill or empty?
Compare the combined filling rate to the draining rate. If filling > draining, net rate is positive and it fills. If draining > filling, net rate is negative and it empties.
What is the first step in the mental checklist for solving CAT time and work problems?
Identify the individual work rates of all agents (people, pipes, etc.), typically as a fraction of the total work per unit time.
In the CAT strategy checklist, when should you break a problem timeline into segments?
When there are multiple periods with different constant conditions, such as workers joining/leaving or rates changing at specific times.
According to the wage proportionality principle, if A is twice as efficient as B, how will their wages be distributed for the same work?
A receives twice the wages of B, because wages are proportional to the work done (efficiency), not the time taken.
If 8 workers can complete a job in 10 days, how many days would 5 workers take to complete the same job, assuming constant efficiency?
Total work = 8 workers * 10 days = 80 worker-days. 5 workers would take 80 / 5 = 16 days.
