CAT Concept of Efficiency and Wages - Practice Questions & MCQ

Definition: Efficiency relates to the capability of a worker (or machine) in terms of the amount of work done per unit time. When relating efficiency to wages, we're often dealing with problems where payment is made based on the amount of work done or efficiency of the worker. This intertwining of efficiency with wages provides a deeper dimension to problems in 'Time and Work'.

Solved Examples:

A can complete a task in 10 days and B in 15 days. They work together for 5 days and receive a combined wage of ₹3000. How should the wage be divided between A and B based on their efficiencies?

Solution:

1. Identify the Total Work (Using Concept 1): Using the LCM method for 10 and 15, we get 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. Calculate Work Done by Each in 5 Days:

   - Work done by A in 5 days = 3 units/day × 5 days = 15 units

   - Work done by B in 5 days = 2 units/day × 5 days = 10 units

4. Determine Share Based on Efficiency:

   Total units of work done in 5 days = 15 units + 10 units = 25 units

   - A’s share = (15 units/25 units) × ₹3000 = ₹1800

   - B’s share = (10 units/25 units) × ₹3000 = ₹1200

Tips and Tricks:

1. Work Equates to Money: In these problems, the work done by an individual directly translates to their monetary compensation. The more efficient, the more they earn.

2. Normalise Before Dividing: It's essential to determine the collective work or efficiency before diving into individual shares. It simplifies the division process.

3. Always Validate: After dividing the wages, always cross-check to ensure the combined wages match the given amount.

Application of Previous Concepts:

- Using Concept 1 for Total Work: Recognize the total quantum of work to understand the scale at which workers operate.

- Employing Concept 2 for 1 Day Work: Find out the efficiency of each worker in terms of work done per day. This becomes the rate at which they earn.

- Relate to Concept 4 When Multiple Entities Work: If there are more than two entities, the methodology remains consistent. Aggregate their work done, and then divide wages proportionately

Efficiency and Wages problems, though they involve an additional layer of wage calculation, fundamentally stick to the principles of 'Time and Work'. Understanding that wage division is a direct consequence of work done makes these problems approachable and solvable. As always, practising such problems will solidify understanding and improve speed.