Jagdish can build a wall in 10 days. Narender can build the same wall in 12 days while sumit takes 15 days to do the same job. Which two of them should be employed to finish the job in 6 days? 

Jagdish can build a wall in 10 days. Narender can build the same wall in 12 days while sumit takes 15 days to do the same job. Which two of them should be employed to finish the job in 6 days?

Jagdish and Narendar will do it in 6 days.

To determine which two workers should be employed to finish the job in 6 days, we need to calculate the portion of the wall each worker can build per day. Then, we select the two workers with the highest combined output.

Let's denote:

• Jagdish's rate of work as J (walls per day)
• Narender's rate of work as N (walls per day)
• Sumit's rate of work as S (walls per day)

We can calculate their individual rates of work using the given information:

• Jagdish completes 1 wall in 10 days, so his rate is 1/10 walls per day (J = 1/10).
• Narender completes 1 wall in 12 days, so his rate is 1/12 walls per day (N = 1/12).
• Sumit completes 1 wall in 15 days, so his rate is 1/15 walls per day (S = 1/15).

Now, we can find the combined rate of work for each pair of workers:

• Jagdish and Narender: J + N
• Jagdish and Sumit: J + S
• Narender and Sumit: N + S

We'll calculate these rates:

• Jagdish and Narender: (1/10) + (1/12) = (6/60) + (5/60) = 11/60 walls per day
• Jagdish and Sumit: (1/10) + (1/15) = (6/60) + (4/60) = 10/60 walls per day
• Narender and Sumit: (1/12) + (1/15) = (5/60) + (4/60) = 9/60 walls per day

Now, we can see which pair has the highest combined rate:

• Jagdish and Narender: 11/60 walls per day
• Jagdish and Sumit: 10/60 walls per day
• Narender and Sumit: 9/60 walls per day

The pair with the highest combined rate is Jagdish and Narender, so they should be employed to finish the job in 6 days.

Concepts of Time and Work

The concept of time and work is a fundamental aspect of various fields including physics, economics, project management, and everyday life. Here's an overview of the concepts:

1. Time:

   • Time is a fundamental dimension that measures the sequence of events, the duration of intervals between events, and the rate of change.
   • In physics, time is often treated as a dimension along with space, forming the basis for the concept of spacetime in theories like special and general relativity.
   • Time is often measured in units such as seconds, minutes, hours, days, etc. It can be represented on various scales, including linear time (chronological time) and cyclical time (such as the seasons).
   • Time can be subjective, as experienced by individuals, or objective, as measured by clocks and calendars.

2. Work:

   • In physics, work is defined as the product of force and displacement along the direction of the force. Mathematically, it's represented as W = F * d * cos(θ), where W is work, F is force, d is displacement, and θ is the angle between force and displacement vectors.
   • In everyday language, work often refers to the effort or activity exerted to achieve a particular goal or outcome. This could include physical labor, mental effort, or any other form of exertion.
   • Work is often measured in units such as joules (in physics) or hours (in employment contexts).
   • In economics, work is associated with productivity, labor, and the creation of goods and services.

3. Time and Work Together:

   • In various contexts, understanding the relationship between time and work is essential. For instance:
     • In physics, the concept of power (work done per unit time) relates work and time.
     • In economics, concepts like hourly wages, productivity per hour, and efficiency relate work and time.
     • In project management, understanding the time required to complete tasks (work) is crucial for scheduling and resource allocation.

4. Time Management:

   • Efficient utilization of time is crucial in personal and professional life. Time management involves prioritizing tasks, setting goals, planning schedules, and avoiding time-wasting activities.
   • Techniques such as the Eisenhower Matrix, Pomodoro Technique, and Gantt charts are used to manage time effectively.

5. Work Measurement:

   • Measuring work accurately is essential for productivity assessment, resource allocation, and performance evaluation.
   • Techniques such as time tracking, task analysis, and performance metrics are used to measure work in different contexts.

Understanding the concepts of time and work, and how they intersect, is essential for effective planning, productivity, and goal achievement in various aspects of life and work.