In-Depth: Time and Work

CLAT Application & Relevance

Importance: Low to Medium. While not a primary focus, Time and Work concepts can appear in Data Interpretation caselets. These problems typically involve comparing the efficiency of different individuals or teams in completing a task, such as drafting documents, reviewing cases, or processing applications. The key is understanding efficiency and combined work rates.

How it's tested: Calculating combined time taken by multiple entities; finding efficiency of an individual from group work; problems involving pipes and cisterns (similar logic to Time & Work).

Section 1: Core Concepts & Formulas

Time and Work problems deal with the rate at which work is done. The core idea is that the total work is constant, and it can be completed by varying the number of workers or their efficiency.

Fundamental Relationship

Work = Efficiency × Time
Derived: Efficiency = Work / Time (Work done per unit of time)
Derived: Time = Work / Efficiency

Often, 'Total Work' is assumed as '1 unit' or a convenient LCM.

Key Concepts & Techniques

Individual's Work Rate: If a person can complete a job in 'N' days, then their 1 day's work (efficiency) is 1/N of the total work.
Combined Work Rate: If multiple people work together, their individual work rates (per day/hour) are added to find the combined work rate.
- If A does a job in 'x' days and B does it in 'y' days, together they do (1/x + 1/y) work per day.
- Time taken together = 1 / (1/x + 1/y) = (x*y) / (x+y) days.
LCM Method (Most Efficient for multiple workers):
1. Assume the 'Total Work' to be the Least Common Multiple (LCM) of the individual times taken.
2. Calculate the 'Efficiency' (units of work per day/hour) for each person: Efficiency = Total Work / Time Taken.
3. Use these efficiencies to solve the problem (e.g., add them for combined work, subtract for negative work like leaks).
Men-Days Formula: M1*D1*H1/W1 = M2*D2*H2/W2 (where M=Men, D=Days, H=Hours/day, W=Work). Useful for problems comparing different groups.

Section 2: Solved CLAT-Style Examples

Example 1: Combined Work Rate (Caselet)

Passage Context: An experienced lawyer can draft a legal brief in 20 hours. A junior lawyer, working alone, takes 30 hours to draft the same brief.

Question: "If they both work together on the brief, how many hours will it take them to complete it?"

Detailed Solution (using LCM Method):
1. Total Work: Assume Total Work = LCM of 20 and 30 = 60 units (e.g., 60 pages to draft).
2. Calculate Individual Efficiencies: Experienced Lawyer's Efficiency = 60 units / 20 hours = 3 units/hour. Junior Lawyer's Efficiency = 60 units / 30 hours = 2 units/hour.
3. Calculate Combined Efficiency: Combined Efficiency = 3 units/hour + 2 units/hour = 5 units/hour.
4. Time Taken Together: Time = Total Work / Combined Efficiency = 60 units / 5 units/hour = 12 hours.
Answer: It will take them 12 hours to complete the brief together.

Example 2: Pipes and Cisterns (Application of Time & Work)

Passage Context: A large water tank that supplies water to a law college has two inlet pipes, A and B, and one outlet pipe, C. Pipe A can fill the tank in 10 hours. Pipe B can fill it in 15 hours. Pipe C can empty the full tank in 12 hours.

Question: "If all three pipes are opened simultaneously, how long will it take to fill the empty tank?"

Detailed Solution (using LCM Method):
1. Total Work (Capacity of Tank): LCM of 10, 15, and 12 = 60 units (e.g., 60 liters).
2. Calculate Individual Rates (Efficiency): Pipe A (filling) = 60 units / 10 hours = +6 units/hour. Pipe B (filling) = 60 units / 15 hours = +4 units/hour. Pipe C (emptying) = 60 units / 12 hours = -5 units/hour (negative because it's emptying).
3. Calculate Combined Rate (Net Efficiency): Combined Rate = A's rate + B's rate + C's rate = 6 + 4 - 5 = 5 units/hour.
4. Time Taken Together: Time = Total Work / Combined Rate = 60 units / 5 units/hour = 12 hours.
Answer: It will take 12 hours to fill the tank if all three pipes are opened simultaneously.