Understanding Time and Work Concept Questions

The Time and Work concept is a vital component of the Quantitative Aptitude section in the Common Law Admission Test (CLAT). This topic assesses your ability to solve problems related to the allocation of tasks, working rates and completion times. 

Grasping the Fundamentals

Before we delve into solving Time and Work problems, let’s establish the foundational concepts:

1. Work Unit

Work is often measured in terms of “work units.” One work unit represents the amount of work a person or a machine can complete in a given time.

2. Time and Work Relationship

The relationship between time and work is inversely proportional. In other words, if the number of workers remains constant, the time taken to complete a task decreases as the work rate increases and vice versa.

3. Work Rate

Work rate refers to the speed at which an individual or a group completes a task. It is usually measured in work units per unit of time.

4. Combined Work

When multiple individuals or entities work together to complete a task, their combined work rate is the sum of their individual work rates.

Solving Time and Work Problems: Concepts and Examples

Example 1: One Person’s Work Rate

Question: If John can complete a painting job in 8 hours, what part of the job can he complete in 2 hours?

Solution:

John’s work rate is 1 job in 8 hours, which is 1/8 of the job per hour.

In 2 hours, John can complete 1/8 × 2 = 1/4 of the job.

Example 2: Multiple Workers with Different Work Rates

Question: If Jane can build a wall in 12 hours and Mark can build it in 8 hours, how long will they take together?

Solution:

Jane’s work rate is 1 job in 12 hours, which is 1/12 of the job per hour.

Mark’s work rate is 1 job in 8 hours, which is 1/8 of the job per hour.

Their combined work rate is 1/12 + 1/8 = 5/24 of the job per hour.

They will complete the job in 24/5 hours, which is approximately 4.8 hours.

Example 3: Work Fraction with Changing Work Rates

Question: A hose can fill a tank in 6 hours and a pump can empty it in 4 hours. If both are operated together for 2 hours and then the pump is turned off, how much of the tank will be filled?

Solution:

The hose’s work rate is 1 tank in 6 hours, which is 1/6 of the tank per hour.

The pump’s work rate is 1 tank in 4 hours, which is 1/4 of the tank per hour.

Together, their combined work rate is 1/6 – 1/4 = 1/12 of the tank per hour.

In 2 hours, the combined work will complete 1/12 × 2 = 1/6 of the tank.

Strategies for Tackling Time and Work Problems

Approaching Time and Work problems requires logical thinking and the ability to manipulate work rates and time. Here are some strategies to help you navigate through these problems effectively:

1. Set Up Equations

Translate the given information into mathematical equations that represent the relationship between work rates, time and the portion of work completed.

2. Use LCM

When dealing with fractions of work rates, use the least common multiple (LCM) of the denominators to find a common work rate.

3. Divide and Conquer

Break down complex problems into simpler steps. Solve for partial work done in a given time and then combine the results to find the complete solution.

4. Check Reasonability

After solving, check if your answer makes sense. For example, the time taken should be a positive value and the completed work fraction should be between 0 and 1.

5. Regular Practice

Practice a variety of Time and Work problems to enhance your problem-solving skills and increase your speed and accuracy.