Short Answer:
The inverse relation between time and efficiency means that when efficiency increases, the time taken to complete work decreases, and when efficiency decreases, the time taken increases. Both move in opposite directions.
In simple words, a faster worker (more efficient) finishes work in less time, while a slower worker (less efficient) takes more time. This relation is very useful in solving time and work problems.
Detailed Explanation:
Inverse relation between time and efficiency
The inverse relation between time and efficiency is a key concept in time and work. It explains how the speed of working affects the time required to complete a task. Efficiency shows how much work is done in one unit of time, while time shows how long it takes to finish the entire work.
When total work is fixed, time and efficiency always have an inverse relationship. This means that if one increases, the other decreases. This simple idea helps in solving many mathematical problems related to work and time.
Meaning of inverse relation
Inverse relation means that two quantities change in opposite directions. When one increases, the other decreases, and when one decreases, the other increases.
In this case, if efficiency becomes higher, the worker can do more work in less time, so the time required becomes less. On the other hand, if efficiency becomes lower, the worker takes more time to complete the same work.
For example, if a worker doubles their efficiency, they will take half the time to complete the work. This clearly shows the inverse relation.
Mathematical explanation
The relation between time and efficiency can be explained using the formula:
Time = Work ÷ Efficiency
Here, if the work remains constant, time depends only on efficiency. If efficiency increases, the value of time decreases. If efficiency decreases, the value of time increases.
For example, if total work is 1 unit and efficiency is 1/4, then time taken is 4 days. If efficiency increases to 1/2, then time reduces to 2 days.
This formula clearly shows how time changes when efficiency changes.
Effect of increase in efficiency
When efficiency increases, the worker completes more work in one unit of time. This reduces the total time required to finish the work.
For example, if a worker improves their skills or uses better tools, they can work faster. As a result, they complete the same task in less time.
This is why higher efficiency is always preferred in real-life work situations.
Effect of decrease in efficiency
When efficiency decreases, the worker does less work in the same time. This increases the total time required to complete the work.
For example, if a worker is tired or lacks proper resources, their efficiency may go down. This will make them take more time to finish the task.
This shows that lower efficiency leads to longer working time.
Use in solving problems
This inverse relation is very useful in solving time and work problems. It helps in finding unknown values easily. For example, if we know how efficiency changes, we can quickly calculate the new time required.
It is also helpful when comparing workers or when workers join or leave the task. By using this concept, we can adjust the time accordingly.
This relation is widely used in exams and practical calculations.
Real life importance
The inverse relation between time and efficiency is seen in daily life. In offices, industries, and schools, people try to improve efficiency to save time.
For example, a skilled worker finishes tasks faster than an unskilled worker. Similarly, students who study efficiently complete their work in less time.
This concept helps in better time management, planning, and increasing productivity.
Conclusion:
The inverse relation between time and efficiency means that both move in opposite directions. Higher efficiency leads to less time, and lower efficiency leads to more time. This simple but important concept helps in solving time and work problems and is useful in everyday life.