CAT Concept of negative Work - Practice Questions & MCQ

Definition: This concept refers to scenarios in which an entity undoes or negatively impacts the progress of a task. In essence, the work done by this entity is subtracted from the progress, as opposed to being added. This typically arises in problems where one entity is constructing or performing a task while another is deconstructing or opposing it.

Solved Examples:

A can build a wall in 5 days, but B can tear it down in 10 days. If A starts building the wall and they work on alternate days with B starting the next day after A, in how many days will the wall be completed?

Solution:

1. Identify the Total Work (Using Concept 1): Using the LCM method, LCM of 5 and 10 is 10. Let's assume the total work (wall) is 10 units.

2. Determine 1 Day Work (Using Concept 2):

   - A’s 1-day work (constructing) = 10 units / 5 days = 2 units/day

   - B’s 1-day work (deconstructing) = -10 units / 10 days = -1 unit/day (Note the negative sign, indicating B is undoing the work)

3. Combined Work for Two Days:

   In two days, A will construct for a day, and B will deconstruct the next.

   Total work done in 2 days = A's 1-day work + B's 1-day work = 2 units - 1 unit = 1 unit.

4. Calculate the Number of Cycles and Remaining Work:

   For every 2 days, only 1 unit of the wall is effectively built. To build 10 units, it will take 20 days (10 cycles of 2-day work).

Tips and Tricks:

1. Watch Out for Negative Signs: Always remember to assign a negative sign for entities doing negative work. This ensures correct calculations and avoids mistakes.

2. Analyse the Net Impact: Instead of looking at individual days, try to analyse the net impact over a set of days. This gives a clearer picture and simplifies calculations.

3. Endgame Analysis: In some problems, the final days might require a different approach, especially if the negative work entity might completely undo the work. Be vigilant during the endgame.

Application of Previous Concepts:

- Using Concept 1 for Total Work: As always, start by determining the total work using the LCM method or other relevant methods.

- Employing Concept 2 for 1 Day Work: With the total work known, we derive the 1-day work for each entity. Ensure to take the negative sign for entities performing negative work.

- Combining with Concept 3: As the problem involved alternate days, we used the knowledge from Concept 3 to determine work over a cycle of days.

Negative work problems can initially seem counterintuitive, but with a clear understanding of how each entity affects the task, they become manageable. Practice and structured thinking are key.