Short Answer:

Efficiencies of two workers are compared by checking how much work each one can complete in the same time or how much time each one takes to complete the same work. The worker who completes more work in less time is more efficient.

In simple terms, we usually compare efficiencies using one day work. The worker who has a higher one day work value is more efficient. This method makes comparison easy and clear.

Detailed Explanation:

Compare efficiencies of workers

Comparing the efficiencies of two workers is an important concept in time and work. It helps us understand who is faster and who can complete more work in less time. Efficiency shows the speed of working, so comparing efficiency means comparing the working speed of different people.

There are simple methods to compare efficiencies. The most common ways are by comparing time taken to complete the same work or by comparing the amount of work done in the same time. Both methods give the same result and are widely used in solving problems.

Comparing using time taken

One of the easiest ways to compare efficiencies is by looking at the time taken by each worker to complete the same work. If one worker takes less time, it means they are more efficient.

For example, if Worker A completes a job in 5 days and Worker B completes the same job in 10 days, then Worker A is more efficient. In fact, Worker A is twice as efficient as Worker B because they take half the time.

This method is simple and commonly used because time is usually given in problems.

Comparing using one day work

Another important method is comparing one day work. One day work means the fraction of total work completed in one day. It directly shows efficiency.

For example, if Worker A completes 1/5 of the work in one day and Worker B completes 1/10, then Worker A is more efficient because they complete more work in one day.

The worker with the higher value of one day work is always more efficient. This method is very useful when dealing with fractions.

Ratio of efficiencies

Efficiencies of two workers can also be compared using ratios. The ratio of efficiency is the inverse of the ratio of time taken when total work is the same.

For example, if Worker A takes 4 days and Worker B takes 8 days to complete a job, then the ratio of their efficiencies is:

Efficiency of A : Efficiency of B = 8 : 4 = 2 : 1

This means Worker A is twice as efficient as Worker B.

This method is helpful in solving problems where ratio is required.

Using common work value

Sometimes, we take total work as a common number, like the LCM of given times, to avoid fractions. Then we calculate how much work each worker does per day.

For example, if one worker takes 6 days and another takes 3 days, we can take total work as 6 units. Then the first worker does 1 unit per day, and the second does 2 units per day. This shows that the second worker is more efficient.

This method makes calculations easier and more clear.

Role in combined work

Comparing efficiencies is very useful when workers work together. It helps us understand how much each person contributes to the total work.

For example, if one worker is twice as efficient as another, then their contribution will also be double. This helps in dividing work properly and calculating total time required.

It is also useful when workers join or leave the work at different times.

Importance in real life

Comparing efficiencies is important in real life as well. In workplaces, employers compare workers to find who performs better. In daily life, we compare our own efficiency to improve our performance.

For example, if a student completes homework faster than others, they are considered more efficient. Similarly, in industries, efficient workers help complete tasks quickly and increase productivity.

Understanding efficiency comparison helps in better planning and achieving goals faster.

Conclusion:

Efficiencies of two workers can be compared by checking time taken, one day work, or using ratios. The worker who does more work in less time is more efficient. This concept is very useful in solving time and work problems and in improving productivity.