CAT Two or more persons working together - Practice Questions & MCQ

Definition: This concept focuses on understanding how tasks are completed when two or more entities (persons, machines, etc.) work together simultaneously on a task, leading to a combined efficiency.

Solved Examples:

A can complete a task in 10 days, and B can complete it in 15 days. If both A and B work together, how long will it take them to finish the task?

Solution:

1. Identify the Total Work (Using Concept 1): LCM of 10 and 15 is 30. Let's assume the total work to be 30 units.

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

- A’s 1-day work = 30 units / 10 days = 3 units/day

 - B’s 1-day work = 30 units / 15 days = 2 units/day

3. Combined 1 Day Work:

Working together, they can complete = A's 1-day work + B's 1-day work = 3 units + 2 units = 5 units/day.

4. Calculate Time Together:

Total Work / Combined 1-day work = 30 units / 5 units/day = 6 days.

Tips and Tricks:

1. Combine Efficiencies: When multiple entities work together, their efficiencies add up. Always combine their 1-day work to get the total work done when they're together.

2. Avoid Over-Complicating: If more than two entities are involved, the method remains the same. Determine each entity's 1-day work and sum them up.

3. Beware of Reduced Efficiencies: Sometimes problems might introduce conditions where two entities working together might reduce each other's efficiency. Always read the problem statement carefully.

Application of Previous Concepts:

- Using Concept 1 for Total Work: We always start by determining the total work, often using the LCM method for ease of calculation.

- Employing Concept 2 for 1 Day Work: Once we have the total work, it's essential to know the rate at which each entity works, so we determine each one's 1-day work.

- Applying Combined Efficiency: With the 1-day work of each entity known, it's a matter of simple addition to get their combined efficiency.

Mastering this concept requires understanding individual efficiencies and then combining them. As always, practice makes perfect. Approach each problem systematically, and it will soon become second nature to solve such questions.