Short Answer:

Combined efficiency is calculated by adding the efficiencies or one day work of all workers who are working together. It shows how much total work is completed by the group in one unit of time, usually one day.

In simple words, first find how much work each person does in one day, then add all those values. The result is the combined efficiency, which helps to find how quickly the group can complete the work.

Detailed Explanation:

Combined efficiency calculation

Combined efficiency calculation is an important concept in time and work. It helps us find how much work is done when two or more workers work together. Instead of solving each worker’s work separately, we combine their efficiencies to make the process simple and faster.

Efficiency means the work done in one unit of time, usually in one day. When workers work together, their efficiencies are added to get the total efficiency of the group. This combined value shows how much work the group can complete in one day.

Finding individual efficiency

The first step in calculating combined efficiency is to find the efficiency of each worker. This is usually done by taking total work as 1 unit. If a worker completes the work in a certain number of days, then their efficiency is the fraction of work done in one day.

For example, if a worker completes a task in 5 days, their efficiency is 1/5. If another worker completes the same task in 10 days, their efficiency is 1/10.

This step is important because we need individual efficiencies before adding them.

Adding efficiencies

After finding individual efficiencies, we add them together to get the combined efficiency. This gives the total work done in one day by all workers together.

For example, if one worker has efficiency 1/5 and another has 1/10, then combined efficiency is:

1/5 + 1/10 = 3/10

This means the group completes 3/10 of the total work in one day.

This step is the main part of the calculation.

Finding total time using combined efficiency

Once we know the combined efficiency, we can find the total time required to complete the work. Since total work is taken as 1 unit, we divide total work by combined efficiency.

For example, if combined efficiency is 3/10, then total time required is:

Time = 1 ÷ (3/10) = 10/3 days

This helps in solving problems where we need to find how long a group will take to finish the work.

Use of LCM method

Sometimes, working with fractions becomes difficult. In such cases, we use the LCM method to simplify calculations. We take total work as the LCM of the given time values.

For example, if one worker takes 4 days and another takes 6 days, we take total work as 12 units. Then the first worker does 3 units per day, and the second does 2 units per day.

Their combined efficiency becomes 5 units per day. This method avoids fractions and makes calculations easier.

Workers with different efficiencies

In many problems, workers have different efficiencies. Some may work faster, and others slower. In such cases, we still follow the same method: find each worker’s efficiency and then add them.

For example, if one worker is twice as efficient as another, we can represent their efficiencies in a ratio and then calculate their combined efficiency accordingly.

This helps in solving more complex problems.

Importance in real life

Combined efficiency is very useful in real life. In construction, multiple workers work together to complete buildings faster. In offices, teams work together to complete projects on time.

In daily life, people share tasks like cleaning or cooking to finish work quickly. By combining efforts, work becomes easier and faster.

This concept shows the importance of teamwork and proper planning.

Conclusion:

Combined efficiency is calculated by adding the individual efficiencies of all workers. It helps us find how much work a group can complete in one day and how long they will take to finish a task. This concept is very useful in both mathematics and real life.