Work, Wages and Time

Last Updated : 21 Aug, 2025

Work refers to the physical or mental effort exerted by an individual to produce goods or provide services in exchange for compensation (wages) or other benefits.

Wage is the monetary payment an employee receives for their labor, typically calculated on an hourly, daily, or piece-rate basis.

Time refers to the duration or period required to complete a specific task or amount of work.

This article will provide you with comprehensive explanations and examples that are easy to follow.

Fundamental Concepts and Formulas

If a person can do a piece of work in ‘n’ days, then in one day, the person will do ‘1/n’ work. Conversely, if the person does ‘1/n’ work in one day, the person will require ‘n’ days to finish the work.
Work Equivalence: The work done by people can be written mathematically as the multiplication of the rate at which the work is done and the time taken to complete the work.

If two people work at different rates and for different times, the work done by each can be equated by multiplying their rate of work and the time they worked. So, the total work done in both cases will be the same.
Work done = (Rate of work) x (Time)
Now provided work remains the same,
R₁T₁ = R₂T₂
Now, Rate of Work = (Number of Workers) x (Number of Days)
M₁D₁T₁ = M₂D₂T₂
where,
M = Number of workers
D = Number of days
R = Rate of Work

In questions where there is a comparison of work and efficiency, we use the formula below:

MT₁ D₁ H₁ E₁ / W₁  = M₂ D₂H₂E₂/ W₂
where,
H = Number of working hours in a day
E = Efficiency of workers
W = Units of work completed
Total work = No. of Days x Efficiency

If we increase the number of workers (M) or days (D), the work done also increases proportionally.
If we increase the number of hours per day (H) or the efficiency of workers (E), it also contributes to completing more work.

For Example: A painter can complete a job in 6 days working alone. If he works with a helper who is twice as efficient, how long will it take them together to complete the whole job?

Solution:

Painter's rate: R₁ = 1/6 of the job per day.
Helper's rate: R₂ = 2 x R₁ = 2 x (1/6) = 1/3 of the job per day (twice as efficient).
Combined Rate: R₁ + R₂ = 1/6 + 1/3 = 1/2
They complete 1/2 of the job per day.
T = 1/R₁+R₂ = 2
Time together: 2 days
Conclusion: They will finish the job in 2 days.

Shortcut Tricks for work Problems

This trick can be used:

To find the efficiency of a person
To find the time taken by an individual to do a piece of work
To find the time taken by a group of individuals to complete a piece of work
Work done by an individual in a certain time duration
Work done by a group of individuals in a certain time duration

The below image illustrates a shortcut trick for calculating the time taken by two individuals, A and B, to complete a task together, based on their individual work rates.

No. of days:

A takes 20 days to complete the work.
B takes 30 days to complete the work.

Efficiency:

A's efficiency is represented as 3 units of work per day.
B's efficiency is represented as 2 units of work per day.

Work:

The total work is calculated as the Least Common Multiple (LCM) of 20 and 30, which is 60 units.

The formula used to find the combined time taken by A and B to complete the work is:

Time = Total Work / (Efficiency of A + Efficiency of B)
Substituting the values: Time = 60 / (3 + 2) = 60 / 5 = 12 days.

Trick to calculate combine work rate

The below image demonstrates a shortcut trick for calculating the combined work rate of individuals A, B and C based on their individual work days.

No. of days:

A + B together take 18 days to complete the work (efficiency 4 units/day).
A + B together take 24 days to complete the work (efficiency 3 units/day).
A + B together take 36 days to complete the work (efficiency 2 units/day).

Efficiency:

The efficiency values (4, 3, 2) represent the work units completed per day by A and B together for the respective time periods.

Work:

The total work is calculated as the Least Common Multiple (LCM) of 18, 24, and 36, which is 72 units.
Work done by A: A's efficiency is 1.5 units/day, time taken = 72 / 1.5 = 48 days.
Work done by B: B's efficiency is 2.5 units/day, time taken = 72 / 2.5 = 28.8 days.
Work done by C: C's efficiency is 0.5 units/day, time taken = 72 / 0.5 = 144 days.