Work Efficiency: Formula, Work Rates and Solved Examples
Work efficiency is the amount of work completed by a person in one unit of time. This page explains the work efficiency formula, the relation between efficiency and time, combined work rates, efficiency ratios and shortcut methods used in time and work questions.
What Is Work Efficiency?
Efficiency = Work ÷ Time. In time and work questions, total work is often represented by the LCM of the individual times. If A completes a job in 12 days, A's one-day work or efficiency is 1/12 of the job. For a fixed amount of work, a person taking 6 days is twice as efficient as a person taking 12 days.
Work Efficiency Formula & Tricks
Important Formulas
The formula gives the amount of work completed in one unit of time.
Multiply the work rate by the number of time units to find total work.
For the same work, efficiency and time are inversely proportional.
When people work together, their individual one-unit work rates are added.
Use this formula when the question asks how much more efficient one worker is than another.
Quick Tricks
For the same work, do not compare efficiencies in the same order as time. Reverse the time ratio.
When workers have different completion times, choose the LCM of their times as total units of work. Their daily efficiencies then become whole numbers.
If A is p% more efficient than B, A's efficiency is (100 + p)% of B's efficiency. Therefore, A's time is 100/(100 + p) times B's time.
Work Efficiency Concepts
Efficiency and Time Relationship
If A and B complete the same work in T_A and T_B units of time, then E_A/E_B = T_B/T_A. A lower completion time means a higher efficiency.
Finding Daily Work Rate
If A completes a job in n days, A's one-day work is 1/n. To avoid fractions, take a convenient total work such as the LCM of all completion times and divide it by each worker's time.
Combined Efficiency of Workers
If A completes 1/T_A of the work per day and B completes 1/T_B per day, their combined rate is 1/T_A + 1/T_B. The time taken together is the reciprocal of this combined rate.
Percentage Change in Efficiency and Time
If efficiency rises by p%, the new time is 100/(100 + p) times the old time. If efficiency falls by p%, the new time is 100/(100 − p) times the old time, provided p is less than 100.
Efficiency of Men, Women or Machines
If one man's efficiency is twice one woman's efficiency, then 1 man does the same work as 2 women in the same time. For a group, multiply the number of workers by the efficiency of each worker type and add the rates.
Work Efficiency Video Lessons
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Time and Work Concepts
Understand the core concepts of Time and Work, including how work, time, and efficiency are related in quantitative aptitude problems.
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Work Efficiency Revision Points
Use these rules to solve efficiency-based time and work questions.
- Efficiency = Work ÷ Time.
- For fixed work, efficiency is inversely proportional to time.
- Efficiency ratio A : B = time of B : time of A.
- A worker who completes a job in n days does 1/n of the job per day.
- For combined work, add individual daily work rates.
- If efficiency increases by p%, new time = 100/(100 + p) × old time.
- If efficiency decreases by p%, new time = 100/(100 − p) × old time.
- The LCM of completion times can be used as total work to obtain integer work rates.
Work Efficiency FAQs
What is the work efficiency formula?
Work efficiency = Total work ÷ Time taken. It represents the work completed in one unit of time.
What is the efficiency ratio of two workers who take 8 days and 12 days?
For the same work, the ratio is the inverse of time: 12 : 8 = 3 : 2. The worker taking 8 days is more efficient.
A is 50% more efficient than B. If B takes 18 days, how long does A take?
A's efficiency is 150% of B's, so A's time = 100/150 × 18 = 12 days.
How do you find combined efficiency when A takes 10 days and B takes 15 days?
Combined rate = 1/10 + 1/15 = 1/6 job per day. Therefore, their combined efficiency completes the job in 6 days.
If a worker's efficiency decreases by 25%, what happens to the time taken?
New time = 100/(100 − 25) × old time = 4/3 of the old time. Thus, time increases by one-third.
Can efficiency be expressed in units other than work per day?
Yes. Efficiency may be expressed as jobs per day, units per hour or any other work unit per time unit. The work and time units must be consistent.